Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 42080: Write in simplest form

3 divided by
x^2 + 4x + 3

minus

1 divided by
X^2 - 9
Click here to see answer by PaulAllen65270(19)

Question 42112: Express result in simplest form

5a – 12
Divided by
a^2 – 8a + 15
minus
3a – 2
Divided by
A^2 – 8a + 15
Click here to see answer by psbhowmick(456)

Question 42098: Determine the values of x for any holes in the graph of:
f(x)= (x+3)/x^2+5x+6.
Click here to see answer by AnlytcPhil(958)

Question 41855: Fungicides account for 1/10 of the pesticides used in the U.S. Insecticides account for 1/4 of all the pesticides used in the U.S. The ratio of fungicides to insecticides used in the U.S. can be written 1/10 divided by 1/4. Write this ratio in simplest form.
Click here to see answer by fractalier(1804)

Question 42199This question is from textbook
: Factor the polynomial P(x)= 16x^4-81 completely and find all its zeros.
I factored to (4x^2+9)(4x^2-9) then further to ((2x+3)(2x-3))^2 to get 3/2 and -3/2 both with multiplicity of 2 to equal four zeros. But the solutions given also contain 3i/2 and -3i/2. Also, I'm unsure that the second factoring step is appropriate since by distribution (2x+3)^2 is not equal to 4x^2+9 etc. I'm stumped! Thanks for any help! This question is from textbook

Click here to see answer by psbhowmick(456)

Question 42224: 1. 5 over 2x plus x over 2

2. 4y2(this is y squared) +16y/4y
Click here to see answer by tutorcecilia(2042)

Question 42162: simplify using Synthetic Division, if possible

t^4+10t^3+35t^2+50t+24/t^2+7t+12
Click here to see answer by fractalier(1804)

Question 42311: Divide this fraction
6p - 18
over 9p
divided by
3r - 9
over p^2 + 2p
Should I be simplfying first or is this already done. I need help on this one.
Thanks
Click here to see answer by fractalier(1804)

Question 42312: Find the perimeter of a rectangle
x over 2x - 5 is the length and
8 over 2x - 5 is the width.
What is the perimeter.
Click here to see answer by fractalier(1804)

Question 42318: I have a Final exam tommorow please help. Question: This width of a rectangle is 2cm less than it's length. If the area of the rectangle is 168 cm2 (squared), what is it's width?
i think it's base x height so like x (x-2) = 168 ... x2(sqd) - 2x=168 but then what?!
Click here to see answer by checkley71(8405)

Question 42339: Multiply 2x² - x - 3 3x² - 11x - 20 ——————————————— × ———————————————— 3x² + 7x + 4 4x² - 9

Click here to see answer by AnlytcPhil(958)

Question 42160: Solve the following system of equations:
2x + 4y + 6z = 2
x + 2z = 0
2x + 3y – z = -5
Click here to see answer by venugopalramana(3286)

Question 42387: Solve in simplest form

4y/y^2 + 6y + 5
Plus
2y/y^2-1

Thanks for help
Click here to see answer by vihits13(20)

Question 42473This question is from textbook
: Simplify:
negative square root of 25This question is from textbook

Click here to see answer by Nate(3495)

Question 42472This question is from textbook
: Simplify:
square root of 150This question is from textbook

Click here to see answer by Nate(3495)

Question 42471This question is from textbook
: Simplify:
(x^3/5)(x^2/3)This question is from textbook

Click here to see answer by Nate(3495)

Question 42470This question is from textbook
: Simplify, if possible:
5(square root)18 - 6(square root)2This question is from textbook

Click here to see answer by Nate(3495)

Question 42468This question is from textbook
: Solve:
7 = 8
_ _
x 3This question is from textbook

Click here to see answer by Nate(3495)

Question 42467This question is from textbook
: Simplify:
8
___
2x-4This question is from textbook

Click here to see answer by Nate(3495)

Question 42489: Please help me understand how to complete problems such as
Factor completely:
Thanks
Click here to see answer by rapaljer(3620)

Question 41681: Solve
x^2 - 16x + 64 = 0
Click here to see answer by Nate(3495)

Question 42535: Solve the equation and check for x
x/6 - x/8 = 1
Thanks for help
Click here to see answer by checkley71(8405)

Question 42543: Simplify: (1 + i)/(2 - i).
Thanks
Click here to see answer by fractalier(1804)

Question 42543: Simplify: (1 + i)/(2 - i).
Thanks
Click here to see answer by Nate(3495)

Question 42541: Simplify (y^2 + y - 20)/(y^2 - 2y - 8).
Thanks
Click here to see answer by rapaljer(3620)

Question 42708This question is from textbook INTERMEDIATE ALGEBRA

: Factor completely:
24x2 - 10x – 4
This question is from textbook INTERMEDIATE ALGEBRA

Click here to see answer by stanbon(26259)

Question 42802: A plane flies 720 mi. against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h what is the plane's speed in still air?
Click here to see answer by fractalier(1804)

Question 42795: Can you please help me simplify 1/3^-5 ? Thanks!
Click here to see answer by fractalier(1804)

Question 42735: Factor each expression
a2(b - c)- 16b2 (b - c)

Thank You!!
Click here to see answer by fractalier(1804)

Question 42789: Solve the following for x
2/5 = x-2/20
Thanks
Click here to see answer by Nate(3495)

Question 42810: 9(x-7+8)-2x+8
Click here to see answer by vihits13(20)

Question 42855: The vertices of ΔABC are A(-3,-4), B(-1,3), C(3,-2). The triangle is rotated 90 degrees counterclockwise.
|0-1|
|1 0| is the rotation matrix used. Find the coordinates of C'.
Thank You
Click here to see answer by fractalier(1804)

Question 42883: 3xcubed-12x
______________
6xcubed-24xsquared+24x
Click here to see answer by ilana(236)

Question 42883: 3xcubed-12x
______________
6xcubed-24xsquared+24x
Click here to see answer by fractalier(1804)

Question 42920This question is from textbook INTERMEDIATE ALGEBRA

: Factor the polynomial 4 a 6 b 7 c 5 - 8 a 7 b 5 c 6 , if possible.
This is the answer I came up with and I am not sure if it is right.
4a 7b 6c 6(b2 - 2ac) This question is from textbook INTERMEDIATE ALGEBRA

Click here to see answer by fractalier(1804)

Question 42921This question is from textbook INTERMEDIATE ALGEBRA

: Factor the expression 11(x + y) - 7 t(x + y).

(11 - 7t)(x + y)
this is what i have come up with.This question is from textbook INTERMEDIATE ALGEBRA

Click here to see answer by fractalier(1804)

Question 42922This question is from textbook INTERMEDIATE ALGEBRA

: Factor 5 x 2 + 5 x y + 13 x + 13 y by grouping.

answer: (5y + 13x)(x - y) This question is from textbook INTERMEDIATE ALGEBRA

Click here to see answer by fractalier(1804)

Question 42903: What values for x must be excluded in the following fraction?

5/x+1
Click here to see answer by fractalier(1804)

Question 42942: Factor the polynomial completely.

Click here to see answer by fractalier(1804)

Question 42947: Factor by grouping

Click here to see answer by fractalier(1804)

Question 42944: Factor the trinomial completely.

Click here to see answer by fractalier(1804)

Question 42960: When dividing polynomials by synthetic division,
Example:
f^2 + 7f + 10 / f + 2
Is the answer: f^2 + 5f ?
Because I've looked at examples and the first term in the quotient would be one exponent less than the beginning one. Meaning in the answer of the example, instead of putting f^2, it's just f. I'm not sure if you understand what I mean, but if you could show me step by step how to write the quotient. Thank you!
Click here to see answer by aaaaaaaa(138)

Question 42968: If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
Click here to see answer by jmg(22)

Question 42904: What values for x must be excluded in the following fraction?
x-4/2
Click here to see answer by Nate(3495)

Question 43023: Solve the following system:

Click here to see answer by stanbon(26259)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850