SOLUTION: Can you please help: My son is having trouble Solving rational equations. Here are a few questions he needs help with: 1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2)) 2. c

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Question 72801This question is from textbook
: Can you please help:
My son is having trouble Solving rational equations.
Here are a few questions he needs help with:
1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2))
2. c - (c/3) + (c/5) = 26
3. (1/8) + ((5x) / (x +2)) = (5/2)
4. (k /(k + 1)) + (k/(k - 2)) = 2

5. (10/(2y +8)) - ((7y + 8)/(y^(2) - 16)) = (-8 / (2y - 8))
6. (5/(x+2)) = (-1/(x^(2) +7x+10)) + (3/(-x-5))
Thank you! This question is from textbook

Answer by rmromero(383) (Show Source):
You can put this solution on YOUR website!

Solving rational equations.
Here are a few questions he needs help with:
1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2))
2 1 -4
_______ - ___ = __________ Multiply each term by the LCD x(x+2)
x + 2 x x(x + 2)

2 1 -4
_______ (x(x+2)) - ___ (x(x+2)) = __________ (x(x+2))
x + 2 x x(x + 2)
2x - 1(x + 2) = -4
2x - x - 2 = -4
x -2 = -4
x - 2 + 2 = -4 + 2
x = -2

2. c - (c/3) + (c/5) = 26
c c
c - ___ + ___ = 26 Multiply each term by the LCD = 15
3 5
c c
c (15) - ___ (15) + ___ (15) = 26 (15)
3 5
15c - 5c + 3c = 390 Combine like terms
13c = 390 Divide 13 both sides
c = 30

3. (1/8) + ((5x) / (x +2)) = (5/2)
1 5x 5
_____ + _______ = ___ Mulitply each term by the LCD = 8(x+2)
8 x + 2 2
1 5x 5
_____ (8(x+2)) + _______ (8(x+2)) = ___ (8(x+2))
8 x + 2 2
1(x+2) + 5x(8) = 5(4(x+2)) Multiply (Distribution Property)
x + 2 + 40x = 20x + 40 Combine like terms
41x + 2 = 20x + 40
21x = 38
38
x = ____
21

4. (k /(k + 1)) + (k/(k - 2)) = 2
k k
_____ + ______ = 2 . LCD is (k + 1)(k - 2)
k + 1 k - 2
k k
_____ (k + 1)(k - 2)+ ______ (k + 1)(k - 2) = 2 (k + 1)(k - 2)
k + 1 k - 2
k(k - 2) + k (k + 1) = 2 Mulitply
Combine like terms

k = -4

5. (10/(2y +8)) - ((7y + 8)/(y^(2) - 16)) = (-8 / (2y - 8))
10 7y + 8 -8
______ - _________ = ______
2y + 8 y^2 - 16 2y - 8

10 7y + 8 -8
________ - __________ = ________ LCD = 2 (y-4)(y+4)
2(y + 4) (y-4)(y+4) 2(y - 4)

10 7y + 8 -8
________ (2(y-4)(y+4))- __________ (2(y-4)(y+4))= ________ (2 (y-4)(y+4))
2(y + 4) (y-4)(y+4) 2(y - 4)

10(y - 4) - 2(7y + 8) = -8 (y + 4)
10y - 40 - (14y + 16) = -8y - 32
10y - 40 - 1(14y + 16) = -8y - 32
10y - 40 + 14y - 16 = -8y - 32 Combine like terms
4y - 56 = -8y - 32
12y = 24 divide both sides by 12
y = 2

6. (5/(x+2)) = (-1/(x^(2) +7x+10)) + (3/(-x-5))
5 -1 3
_____ = ______________ + ________
x + 2 x^2 + 7x + 10 -x - 5
5 -1 3
_____ = ______________ + _________ LCD = -1(x + 5)(x + 2)
x + 2 (x + 5)(x + 2) -1(x + 5)

5 -1 3
_____ (-1(x + 5)(x + 2)) = ______________ (-1(x + 5)(x + 2)) + _________ (-1(x + 5)(x + 2))
x + 2 (x + 5)(x + 2) -1(x + 5)

5 (-1(x + 5)) = -1 (-1) + 3 (x + 2)
-5x - 25 = 1 + 3x + 6
-5x - 25 = 3x + 7
-32 = 8x
-4 = x

SOLUTION: Can you please help: My son is having trouble Solving rational equations. Here are a few questions he needs help with: 1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2)) 2. c - (