SOLUTION: Solve the following: {{{(3x/(x^2+5x+6))=(5x/(x^2+2x-3))-(2/(x^2+x-2))}}} I know the LCD is (x+3)(x+2)(x-1) But the answer I came up with is 2x^2 + 11x +6.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the following: {{{(3x/(x^2+5x+6))=(5x/(x^2+2x-3))-(2/(x^2+x-2))}}} I know the LCD is (x+3)(x+2)(x-1) But the answer I came up with is 2x^2 + 11x +6.      Log On


   

Question 907734: Solve the following:
%283x%2F%28x%5E2%2B5x%2B6%29%29=%285x%2F%28x%5E2%2B2x-3%29%29-%282%2F%28x%5E2%2Bx-2%29%29
I know the LCD is (x+3)(x+2)(x-1)
But the answer I came up with is 2x^2 + 11x +6.
Found 2 solutions by KMST, josgarithmetic:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2F%28x%5E2%2B5x%2B6%29%29=%285x%2F%28x%5E2%2B2x-3%29%29-%282%2F%28x%5E2%2Bx-2%29%29
Multiplying both sides of the equal sign times %28x%2B3%29%28x%2B2%29%28x-1%29 ,
you get an equivalent equation, except that you may get some extraneous solution(s) that would make the LCD and some denominator equal to zero.
The equivalent equation and solution follow.
3x%28x-1%29=5x%28x%2B2%29-2%28x%2B3%29
3x%5E2-3x=5x%5E2%2B10x-2x-6
3x%5E2-3x=5x%5E2%2B8x-6
2x%5E2%2B11x-6=0
The polynomial on the left can be factored to get
%282x-1%29%28x%2B6%29=0
So either 2x-1=0--->highlight%28x=1%2F2%29 ,
or x%2B6=0--->highlight%28x=-6%29 .
Both answers are valid since they do not make any denominator equal to zero.

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2F%28x%5E2%2B5x%2B6%29%29=%285x%2F%28x%5E2%2B2x-3%29%29-%282%2F%28x%5E2%2Bx-2%29%29



LCD is %28x%2B2%29%28x%2B3%29%28x-1%29, same as what you found.




%28x-1%29%283x%29=%28x%2B2%29%285x%29-%28%28x%2B3%292%29

3x%5E2-3x=5x%5E2%2B10x-%282x%2B6%29
3x%5E2-3x=5x%5E2%2B10x-2x-6
-2x%5E2-3x-10x%2B2x%2B6=0
-2x%5E2-11x%2B6=0
highlight_green%282x%5E2%2B11x-6=0%29 after multiplying left and right by -1.
FACTORABLE:
highlight_green%28%282x-1%29%28x%2B6%29=0%29
highlight%28x=1%2F2%29 OR highlight%28x=-6%29