Question

Simplify: (r-4) over (r^2-r-6) divided by (4-r) over (r+2)

I know the answer is -1/(r-3), but I can't figure out how to get it there.

Answer 1

Factor (r^2-r-6) first..
(r^2-r-6) = r^2 -3r + 2r - 6 = r ( r-3) + 2 (r-3) = ...?

Answer 2

When I factored (r^2-r-6) I got (r+2)(r-3)

Answer 3

so then, do I multiply both sides of the equation by (r+2)(r-3)over 1?

Answer 4

(r-4) over (r^2-r-6) divided by (4-r) over (r+2)
\[\frac{(r-4)}{(r^2-r-6)} \div \frac{(4-r)}{(r+2)}\]\[=\frac{(r-4)}{(r+2)(r-3)} \div \frac{(4-r)}{(r+2)}\]\[=\frac{(r-4)}{(r+2)(r-3)} \times \frac{(r+2)}{(4-r)}\]\[=\frac{(r-4)}{(r+2)(r-3)} \times \frac{(r+2)}{-(r-4)}\]

Answer 5

It's not an equation...

Answer 6

sry, wrong terminology. not equation, problem

Answer 7

No worries... Do you get it?

Answer 8

so then at the last step, do you just multiply straight across? then re-factor out?

Answer 9

Cancel the common factors.

Answer 10

or wait, the (r+2)'s and the (r-4)'s cancel out.

Answer 11

thank you so much. you were very helpful

Answer 12

Welcome :)