Question

How do you simplify `(3x^2-3x-6)/(x^2-4)`?

Answer 1

`(3(x+1))/(x+2)`

Explanation:

`"factorise the numerator/denominator and "`
`"cancel any common factors"`

`color(magenta)"factor numerator"`

`"take out a "color(blue)"common factor "3`

`rArr3(x^2-x-2)`

`"the factors of - 2 which sum to - 1 are - 2 and + 1"`

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

`color(magenta)"factor denominator"`

`x^2-4" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`rArrx^2-4=x^2-2^2=(x-2)(x+2)`

`rArr(3x^2-3x-6)/(x^2-4)`

`=(3cancel((x-2))(x+1))/(cancel((x-2))(x+2))`

`=(3(x+1))/(x+2)`

`"with restriction "x!=-2`