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)

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

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) (Show Source): You can put this solution on YOUR website!
Problem #1
First of all, is the right side of the equation or is it???? I will assume it's the latter and I will make the same assumption for problem #2.

Note that we can factor first = so we have:
Now we will multiply each term by , 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:
get rid of parens
subtract 3 from both sides
collect like terms
take square root of both sides

Problem #2
we will factor first
Now we will multiply each term by , 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:
get rid of parens
subtract 6 from both sides
collect like terms
multiply both sides by -1
factor

and

Problem #3

We can factor so we have
Now we will multiply each term by , 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:
get rid of the parens
subtract 2y and 8 from both sides
collect like terms
subtract 1 from each side
collect like terms
divide both sides by -4

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

Hope this helps----ptaylor

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