SOLUTION: solve and check the equation for x 5/x+6 + 2/x^2+7x+6 = 3/x+1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve and check the equation for x 5/x+6 + 2/x^2+7x+6 = 3/x+1      Log On


   

Question 94579: solve and check the equation for x
5/x+6 + 2/x^2+7x+6 = 3/x+1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28x%2B6%29 + 2%2F%28x%5E2%2B7x%2B6%29 = 3%2F%28x%2B1%29
:
Factor the quadratic;
5%2F%28x%2B6%29 + 2%2F%28x%2B6%29%28x%2B1%29 = 3%2F%28x%2B1%29
:
Multiply thru by (x+6)(x+1)
(x+6)(x+1)*5%2F%28x%2B6%29 + (x+6)(x+1)*2%2F%28x%2B6%29%28x%2B1%29 = (x+6)(x+1)*3%2F%28x%2B1%29
:
Cancel out the denominators and you 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