SOLUTION: my problem is 5x-8 over x+2 = 5x-1 over x+3. my gcd is (x+2)(x+3) and I know that I multiply everything by it. I come up with 5x^2+15=5X^2+10, then I get 5x^2+5=5x^2, I don't kn

Algebra ->  Rational-functions -> SOLUTION: my problem is 5x-8 over x+2 = 5x-1 over x+3. my gcd is (x+2)(x+3) and I know that I multiply everything by it. I come up with 5x^2+15=5X^2+10, then I get 5x^2+5=5x^2, I don't kn      Log On


   

Question 77029: my problem is 5x-8 over x+2 = 5x-1 over x+3.
my gcd is (x+2)(x+3) and I know that I multiply everything by it. I come up with 5x^2+15=5X^2+10, then I get 5x^2+5=5x^2, I don't know what to do after that, or even if I done it right up to that point. I appreciate your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285x-8%29%2F%28x%2B2%29=%285x-1%29%2F%28x%2B3%29 Start with the given problem
Multiply by the LCD
%285x-8%29%28x%2B3%29=%285x-1%29%28x%2B2%29
5x%5E2%2B15x-8x-24=5x%5E2%2B10x-x-2 foil the parenthesis
5x%5E2%2B7x-24=5x%5E2%2B9x-2 Combine like terms
7x-24=9x-2 Subtract 5x%5E2 from both sides
-24=9x-7x-2 Subtract 7x from both sides
-24%2B2=2x Add 2 to both sides
-22=2x
x=-22%2F2 Divide both sides by 2
x=-11
So x=-11


Check:
%285%28-11%29-8%29%2F%28%28-11%29%2B2%29=%285%28-11%29-1%29%2F%28%28-11%29%2B3%29 Plug in x=-11
%28-55-8%29%2F%28-9%29=%28-55-1%29%2F%28-8%29
%28-63%29%2F%28-9%29=%28-56%29%2F%28-8%29
7=7 works