Question

How do you multiply and simplify `\frac { 10r ^ { 2} - 40r } { r - 9} \cdot \frac { r - 9} { - r ^ { 2} + 13r - 36}`?

Answer 1

`=10/(9-r)`

Explanation:

Factorise each part first and then you can cancel factors that are the same.

`(10r^2-40r)/(r-9) xx (r-9)/(-r^2+13r-36)`

`(10(r-4))/cancel((r-9)) xx cancel((r-9))/(-(r^2-13r+36))" "larr` divide `-1` out

`(10cancel((r-4)))/cancel((r-9)) xx cancel((r-9))/(-(r-9)cancel((r-4))`

`=10/(9-r)`