SOLUTION: How do you subtract 3x/2x-3 - 3x-6/2x^2+x-6?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you subtract 3x/2x-3 - 3x-6/2x^2+x-6?      Log On


   

Question 74501: How do you subtract 3x/2x-3 - 3x-6/2x^2+x-6?
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%283x%2F%282x-3%29%29+-+%28%283x-6%29%2F%282x%5E2%2Bx-6%29%29+
factor the second fraction ... both the numerator and denominator.
+%283x%2F%282x-3%29%29+-+%28%283x-6%29%2F%28%282x-3%29%28x%2B2%29%29%29+
We now need to find common denominators, in this case ... (2x-3)(x+2) ... since the first fraction is only missing the (x+2), multiply the top and bottom by (x+2)

Now that we have common denominators we can place both numerators over a single denominator.
+%283x%28x%2B2%29+-+%283x-6%29%29%2F%28%282x-3%29%28x%2B2%29%29%29+
Distribute the 3x across the first quantity and the negative over the second.
+%283x%5E2+%2B+6x+-+3x+%2B+6%29%2F%28%282x-3%29%28x%2B2%29%29+
combine like terms in the numerator
+%283x%5E2+%2B3x+%2B6%29%2F%28%282x-3%29%28x%2B2%29%29%29+
Factor the numerator
+%283%28x%5E2%2Bx%2B2%29%29%2F%28%282x-3%29%28x%2B2%29%29%29+
This is as simplified as it can get