SOLUTION: I dont understand how to solve this problem: Original Equation: [(x)/(x-3)] - [(2)/(x+8)]= [(78)/(x^2+5x-24)] What I did: Multiplied left side of the equation to get

Question 728569:
I dont understand how to solve this problem:
Original Equation:
[(x)/(x-3)] - [(2)/(x+8)]= [(78)/(x^2+5x-24)]
What I did:
Multiplied left side of the equation to get common denominator:
(x+8)[(x)/(x-3)] - (x-3)[(2)/(x+8)]
I get this when simplified:
[x^2+6x+6/(x^2+5x-24)]=[(78/(x^2+5x-24)]
I mult each side by denom: so...
x^2+6x+6=78
subtract and simplify:
x^2+6x-72=0
But after this step I find that I can not factor it.
If i put no solution in as the answers, it is wrong. When did I go wrong?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
from
[x^2+6x+6/(x^2+5x-24)]=[(78/(x^2+5x-24)]
we get
(x^2+6 x+6)/((x-3) (x+8)) = 78/((x-3) (x+8))
(x^2+6 x-72)/((x-3) (x+8)) = 0
((x-6) (x+12))/((x-3) (x+8)) = 0
x=6
x=-12
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