Question

How do you multiply and simplify `\frac { 1} { x + 2} \cdot \frac { x ^ { 2} - 9x + 20} { 4- x }`?

Answer 1

`(5-x)/(x+2)`

Explanation:

You would factor `x^2-9x+20=(x-5)(x-4)` and substitute it in the expression to get:

`1/(x+2)*((x-5)(x-4))/(4-x)`

Since `(x-4)/(4-x)=-1`, you get:

`1/(x+2)*((x-5)cancel((x-4))^-1)/cancel((4-x))`

`=(5-x)/(x+2)`