Question

Reduce to lowest term. 2x^2- 18/x^2+4x-21​

Answer 1

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

Explanation:

Given

`(2x^2-18)/(x^2+4x-21)` ← factorise numerator and denominator

2x² - 18 ( factor out 2 from each term )

= 2(x² - 9) ← difference of 2 squares

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

and

x² + 4x - 21 = (x + 7)(x - 3) , then

=
`(2(x-3)(x+3))/((x+7)(x-3))` ← cancel common factor (x - 3) on numerator/ denominator

=
`(2(x+3))/(x+7)`