SOLUTION: Hi I need help with rational equations. The Directions say to Factor First then solve the equation. 1. x/(x+3) + 1/(x-1)= 4/ x^2+2x-3 2. 2/(x-1) - x/(x+3)= 6/ x^2+2x-3 3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need help with rational equations. The Directions say to Factor First then solve the equation. 1. x/(x+3) + 1/(x-1)= 4/ x^2+2x-3 2. 2/(x-1) - x/(x+3)= 6/ x^2+2x-3 3      Log On


   

Question 75282: Hi I need help with rational equations. The Directions say to Factor First then solve the equation.
1. x/(x+3) + 1/(x-1)= 4/ x^2+2x-3
2. 2/(x-1) - x/(x+3)= 6/ x^2+2x-3
3. 1/(y^2-16)- 2/(y+4)= 2/(y-4)
If you can help me with these and explain them I would very much appriciate
it. The TextBook I'm using is Algebra 1 Concepts and Skills by McDougal. AND im on Chaper 11.7
thank you.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Problem #1
First of all, is the right side of the equation %284%2Fx%5E2%29%2B2x-3 or is it4%2F%28x%5E2%2B2x-3%29???? I will assume it's the latter and I will make the same assumption for problem #2.
x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%5E2%2B2x-3%29
Note that we can factor first x%5E2%2B2x-3=%28x%2B3%29%28x-1%29 so we have:
x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%2B3%29%28x-1%29 Now we will multiply each term by %28x%2B3%29%28x-1%29, which is the LCM and this will get rid of the fractions
start canceling terms in the numerator and denominator and when we get through, we have:
x%28x-1%29%2B%28x%2B3%29=4 get rid of parens
x%5E2-x%2Bx%2B3=4 subtract 3 from both sides
x%5E2-x%2Bx%2B3-3=4-3 collect like terms
x%5E2=1 take square root of both sides
x=plus+or+minus+1
Problem #2
2%2F%28x-1%29+-+x%2F%28x%2B3%29=+6%2F%28x%5E2%2B2x-3%29 we will factor first
2%2F%28x-1%29-x%2F%28x%2B3%29=6%2F%28x%2B3%29%28x-1%29 Now we will multiply each term by %28x%2B3%29%28x-1%29, which is the LCM and this will get rid of the fractions---same as before but this time I will cancel out terms as we go:
2%28x%2B3%29-x%28x-1%29=6 get rid of parens
2x%2B6-x%5E2%2Bx=6 subtract 6 from both sides
2x%2B6-6-x%5E2%2Bx=6-6 collect like terms
-x%5E2%2B3x=0multiply both sides by -1
x%5E2-3x=0 factor
x%28x-3%29=0
x=0
and
x=3
Problem #3
1%2F%28y%5E2-16%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29
We can factor %28y%5E2-16%29=%28y%2B4%29%28y-4%29 so we have
1%2F%28y%2B4%29%28y-4%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29 Now we will multiply each term by %28y%2B4%29%28y-4%29, which is the LCM and this will get rid of the fractions---same as before but this time I will cancel out terms as we go:
1-2%28y-4%29=2%28y%2B4%29 get rid of the parens
1-2y%2B8=2y%2B8 subtract 2y and 8 from both sides
1-2y-2y%2B8-8=2y-2y%2B8-8 collect like terms
1-4y=0 subtract 1 from each side
1-1-4y=-1 collect like terms
-4y=-1 divide both sides by -4
y=1%2F4

A good drill for you is to plug the answers in and see if they work

Hope this helps----ptaylor