Question

How do you divide `\frac { x ^ { 2} + 3x - 54} { 2x - 12} \div \frac { x ^ { 2} + 18x + 81} { 8x - 24}`?

Answer 1

`color(brown)((4 * (x -3)) / (x + 9)`

Explanation:

`((x^2 + 3x - 54) / (2x - 12)) / ((x^2 + 18x + 81)/(8x - 24))`

`=> ((x^2 + 9x - 6x - 54) / (2 * (x - 6))) / ((x+9)^2 / (8 * (x - 3))`

`=> (cancel((x+9) (x - 6)) * 8 * (x - 3)) / ((x + 9) * cancel((x + 9) * (x - 6)) * 2)`

`=> (cancel(8)^color(red)(4) * (x - 3)) / (cancel2 * (x + 9))`

`color(brown)((4 * (x -3)) / (x + 9)`