perform the indicated operation and simplify:

Question

3x+6 x^2-4
----- divided by -----
4x+12 x-3

Answer 1

(3x+6)/(4x+12) / (x^2 - 4)/(x-3)
first, to divide, we get the reciprocal of the divisor (or the second term/ term at the right) and the operation will be multiplication. reciprocal is just interchanging the numerator and denominator terms. thus,
(3x+6)/(4x+12) * (x-3)/(x^2 - 4)
factoring out each term,
[3(x+2)]/[4(x+3)] * (x-3)/[(x-2)(x+2)]
we can cancel out x+2:
[3(x-3)]/[4(x+3)(x-2)] or
(3x - 9)/(4x^2 + 4x - 24)

hope this helps~ :)