Question 57032
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)