How do you divide #\frac { 3x ^ { 2} - 14x - 24} { 4x ^ { 2} - 81} \div \frac { 4x ^ { 2} - 25x + 6} { 8x ^ { 2} + 34x - 9}#?

1 Answer
Shell
Dec 3, 2016

#frac{(3x+4)}{(2x-9)}#

Explanation:

#frac{3x^2-14x-24}{4x^2-81}-:frac[4x^2-25x+6}{8x^2+34x-9}#

To divide one fraction by another, multiply the first by the reciprocal of the second.

#frac{3x^2-14x-24}{4x^2-81} * frac{8x^2+34x-9}[4x^2-25x+6}#

Factor each numerator and denominator.

#frac{(3x+4)(x-6)}{(2x-9)(2x+9)} * frac{(4x-1)(2x+9)}{(4x-1)(x-6)}#

Cancel factors (you can cancel vertically or diagonally, but not horizontally).

#frac{(3x+4)color(red)cancel((x-6))}{(2x-9)color(magenta)cancel((2x+9))} * frac{color(blue)cancel((4x-1))color(magenta)cancel((2x+9))}{color(blue)cancel((4x-1))color(red)cancel((x-6))}#

#frac{(3x+4)}{(2x-9)}#

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