Question

How do you multiply and simplify `\frac { x ^ { 2} - 5x + 6} { x + 2} \cdot \frac { 2x ^ { 2} + 3x - 2} { x ^ { 2} + 5x - 14}`?

Answer 1

`(x^2-5x+6)/(x+2)`

Explanation:

`(x^2-5x+6)/(x+2) * (2x^2+3x+2)/(x^2+5x-14)`

factorise quadratic expressions:

`(x^2-5x+6):`
`-3 - 2=-5`
`-3*-2 = 6`

`(x^2-5x+6)=(x-3)(x-2)`

`(x^2+5x-14):`
`7 - 2=5`
`7 * -2 = -14`

`(x^2+5x-14)=(x+7)(x-2)`

`(2x^2+3x-2) = (2x-1 )(x+2 )`

insert simplified expressions into question:

`((x-3)(x-2))/(x+2) * ((x+7)(x-2))/((x+7)(x-2))`

cancel out fractions:

`((x-3)cancel(x-2))/(x+2) * (cancel(x+7)(x-2))/(cancel(x+7)cancel(x-2))`

this leaves you with `(x-3)/(x+2) * (x-2)`

`(x-3)(x-2) = x^2-5x+6`

final answer:`(x^2-5x+6)/(x+2)`