SOLUTION: You guys are great. Please help . Reduce /simplify the fractions or square root 1. 14/21 2. AB^2C/A^3BC 3.(x-2)(x-3)/2(x-3) 4.2x^2-2x-4/x^2-1 5. Square root

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: You guys are great. Please help . Reduce /simplify the fractions or square root 1. 14/21 2. AB^2C/A^3BC 3.(x-2)(x-3)/2(x-3) 4.2x^2-2x-4/x^2-1 5. Square root       Log On


   

Question 192966: You guys are great. Please help . Reduce /simplify the fractions or square root
1. 14/21

2. AB^2C/A^3BC

3.(x-2)(x-3)/2(x-3)

4.2x^2-2x-4/x^2-1

5. Square root of 49

6. Square root of 18
7. 36/64 this question has line on the top and sides of both.
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1
Solved by pluggable solver: Reducing Fractions Calculator
In order to reduce 14%2F21, the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal.


In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of 14 and 21 is (note: click here if you need help with finding the GCF). So divide both the numerator and denominator by



In other words, to reduce the fraction you do this
%28numerator%2FGCF%29%2F%28denominator%2FGCF%29=Reduced_Fraction



%2814%2F%29%2F%2821%2F%29 Plug in the numerator, denominator, and the GCF


%282%29%2F%2821%2F%29 Now divide 14 by to get 2. This is now the new numerator.


2%2F3 Now divide 21 by to get 3. This is now the new denominator.



So

%2814%2F%29%2F%2821%2F%29=2%2F3




This means that 14%2F21 reduces to 2%2F3



In other words, 14%2F21=2%2F3








# 2

%28AB%5E2C%29%2F%28A%5E3BC%29 Start with the given expression


%28A%2AB%2AB%2AC%29%2F%28A%2AA%2AA%2AB%2AC%29 Factor


Highlight the common terms.


Cancel out the common terms.


%28B%29%2F%28A%2AA%29 Simplify


B%2F%28A%5E2%29 Multiply


So %28AB%5E2C%29%2F%28A%5E3BC%29=B%2F%28A%5E2%29 where every variable CANNOT equal 0.





# 3

%28%28x-2%29%28x-3%29%29%2F%282%28x-3%29%29 Start with the given expression


%28%28x-2%29highlight%28%28x-3%29%29%29%2F%282%2Ahighlight%28%28x-3%29%29%29 Highlight the common terms.


%28%28x-2%29cross%28%28x-3%29%29%29%2F%282%2Across%28%28x-3%29%29%29 Cancel out the common terms.


%28x-2%29%2F2 Simplify


So %28%28x-2%29%28x-3%29%29%2F%282%28x-3%29%29=%28x-2%29%2F2 where x%3C%3E3



# 4

%282x%5E2-2x-4%29%2F%28x%5E2-1%29 Start with the given expression


%282%28x-2%29%28x%2B1%29%29%2F%28x%5E2-1%29 Factor the numerator


%282%28x-2%29%28x%2B1%29%29%2F%28%28x%2B1%29%28x-1%29%29 Factor the denominator


%282%28x-2%29highlight%28%28x%2B1%29%29%29%2F%28highlight%28%28x%2B1%29%29%28x-1%29%29 Highlight the common terms.


%282%28x-2%29cross%28%28x%2B1%29%29%29%2F%28cross%28%28x%2B1%29%29%28x-1%29%29 Cancel out the common terms.


%282%28x-2%29%29%2F%28x-1%29 Simplify


%282x-4%29%2F%28x-1%29 Distribute


So %282x%5E2-2x-4%29%2F%28x%5E2-1%29=%282x-4%29%2F%28x-1%29 where x%3C%3E-1 or x%3C%3E1




# 5


To find, sqrt%2849%29, let's list the first few perfect squares. To find the perfect squares, just square 0 to get 0, square 1 to get 1, square 2 to get 4, square 3 to get 9, etc...


So the first few perfect squares are:

0%5E2=0, 1%5E2=1, 2%5E2=4, 3%5E2=9, 4%5E2=16, 5%5E2=25, 6%5E2=36, 7%5E2=49, 8%5E2=64, 9%5E2=81, 10%5E2=100


Notice that 7%5E2=49. Remember that the square root "undoes" a square. So sqrt%2849%29=sqrt%287%5E2%29=7 or simply sqrt%2849%29=7




# 6


sqrt%2818%29 Start with the given expression


The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.

So let's list the factors of 18


Factors:
1, 2, 3, 6, 9, 18


Notice how 9 is the largest perfect square, so lets factor 18 into 9*2


sqrt%289%2A2%29 Factor 18 into 9*2

sqrt%289%29%2Asqrt%282%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

3%2Asqrt%282%29 Take the square root of the perfect square 9 to get 3


So the expression sqrt%2818%29 simplifies to 3%2Asqrt%282%29


In other words, sqrt%2818%29=3%2Asqrt%282%29

----------------------------
Check:
Notice if we evaluate the square root of 18 with a calculator we get

sqrt%2818%29=4.24264068711928


and if we evaluate 3%2Asqrt%282%29 we get


3%2Asqrt%282%29=4.24264068711928


This shows that sqrt%2818%29=3%2Asqrt%282%29. So this verifies our answer





# 7

I don't know what you mean here....

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
1) 14/21 divide num & den by 7 =2/3
2) check if this is right problem
(a b^2c) / (a^3bc
to divide common bases, subtract exponents
taking one variable at a time
a^1/a^3 = a6(1-3) = a^(-2) = 1/(a^2)
b^2/b=b^(2-1)=b^1=b
c^1/c^1=c^(1-1)=c^0=1
recombining
answer = B/A^2
3) check to see if correct problem
((x-2)(x-3))/ (2(x-3))
(x-3)/(x-3)=1
(x-2)/2
4) ( 2x^2-2x-4)/(x^2-1)
factor numerator and denominator
((2)(x-2)(x+1))/((x+1)(x-1))
(x+1)/(x+1)=1
(2(x-2))/(x-1)
5) sqrt49=+/- 7
6) sqrt18=sqrt(9*2)=sqrt9*sqrt2=+/- 3sqrt2
7) (36)/(64) dive num & den by 4 = 9/16