SOLUTION: hello, i need help solving this equation and simplying my answer as much as possible, thanks so much! 2x 3 1 ------- - ------ + ------ x^2+x-6 x+

Algebra ->  Systems-of-equations -> SOLUTION: hello, i need help solving this equation and simplying my answer as much as possible, thanks so much! 2x 3 1 ------- - ------ + ------ x^2+x-6 x+      Log On


   

Question 57032: hello, i need help solving this equation and simplying my answer as much as possible, thanks so much!
2x 3 1
------- - ------ + ------
x^2+x-6 x+3 x-2
Found 2 solutions by Cintchr, BGluvsmath:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%2F%28x%5E2%2Bx-6%29+-+3%2F+%28x%2B3%29+%2B+1%2F%28x-2%29+
Factor the denominator of the first fraction
+2x%2F%28x%2B3%29%28x-2%29+-+3%2F+%28x%2B3%29+%2B+1%2F%28x-2%29+
Multiply the 2nd fraction by +%28x-2%29%2F%28x-2%29+ and the 3rd by +%28x%2B3%29%2F%28x%2B3%29+

With the denominators all the same ... combine the numerators
+%282x-3%28x-2%29%2B1%28x%2B3%29%29%2F%28x%2B3%29%28x-2%29+
Distibute through the numerator
+%282x-3x%2B6%2B1x%2B3%29%2F%28x%2B3%29%28x-2%29+
Combine the X terms in the numerator
+%286%2B3%29%2F%28x%2B3%29%28x-2%29+
Combine the constants
+9%2F%28x%2B3%29%28x-2%29+

Answer by BGluvsmath(64) About Me  (Show Source):
You can put this solution on YOUR website!
2x/(x^2+x-6) - 3/(x+3) + 1/(x-2)
To get a common denominator (necessary for adding and subtracting fractions), multiply the 2nd term by x-2 and the 3rd term by x+3:
2x/(x^2+x-6) - 3(x-2)/((x+3)(x-2)) + 1(x+3)/((x-2)(x+3))
(x+3)(x-2) simplifies to x^2+x-6, so:
2x-3(x-2)+(x+3)/(x^2+x-6)
2x-3x+6+x+3/x^2+x-6
The x's cancel out of the numerator, so this simplifies to:
9/(x^2+x-6)