SOLUTION: Solve and check for x. {{{5/(x+6)+2/(x^2+7x+6)=3/(x+1)}}} Could someone show me how to solve this equation, Please.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve and check for x. {{{5/(x+6)+2/(x^2+7x+6)=3/(x+1)}}} Could someone show me how to solve this equation, Please.      Log On


   

Question 95619: Solve and check for x.
5%2F%28x%2B6%29%2B2%2F%28x%5E2%2B7x%2B6%29=3%2F%28x%2B1%29
Could someone show me how to solve this equation, Please.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve and check for x.
5%2F%28x%2B6%29%2B2%2F%28x%5E2%2B7x%2B6%29=3%2F%28x%2B1%29
:
The quadratic in the denominator will factor:
5%2F%28x%2B6%29%2B2%2F%28%28x%2B6%29%28x%2B1%29%29=+3%2F%28x%2B1%29
:
The common denominator is (x+6)(x+1), multiply by that and we have:
5(x+1) + 2 = 3(x+6)
5x + 5 + 2 = 3x + 18
5x + 7 = 3x + 18
5x - 3x = 18 - 7
2x = 11
x = 11/2
:
Check using x = 5.5:
Solve and check for x.
5%2F%285.5%2B6%29%2B2%2F%285.5%5E2%2B7%285.5%29%2B6%29=3%2F%285.5%2B1%29
:
5%2F11.5%2B2%2F%2830.25%2B38.5%2B6%29=3%2F6.5
:
5%2F11.5+%2B+2%2F74.75+=+3%2F6.5
:
.4348 + .02676 = .46154
.46156 ~ .46154