Question

How do you simplify `\frac { x ^ { 3} - 4x } { x ^ { 2} + x - 2}`?

Answer 1

`(x(x-2))/(x-1)`

Explanation:

`"Factorise numerator/denominator"`

`• " numerator "x^3-4x`

`"take out a "color(blue)"common factor of x"`

`=x(x^2-4)`

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

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`rArrx^3-4x=x(x-2)(x+2)`

`• " denominator "x^2+x-2`

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

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

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

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

`=(x(x-2))/(x-1)`

`"with restriction "x!=1`