"factorise the numerator/denominator and "factorise the numerator/denominator and
"cancel any common factors"cancel any common factors
color(magenta)"factor numerator"factor numerator
"take out a "color(blue)"common factor "3take out a common factor 3
rArr3(x^2-x-2)⇒3(x2−x−2)
"the factors of - 2 which sum to - 1 are - 2 and + 1"the factors of - 2 which sum to - 1 are - 2 and + 1
=3(x-2)(x+1)=3(x−2)(x+1)
color(magenta)"factor denominator"factor denominator
x^2-4" is a "color(blue)"difference of squares"x2−4 is a difference of squares
•color(white)(x)a^2-b^2=(a-b)(a+b)∙xa2−b2=(a−b)(a+b)
rArrx^2-4=x^2-2^2=(x-2)(x+2)⇒x2−4=x2−22=(x−2)(x+2)
rArr(3x^2-3x-6)/(x^2-4)⇒3x2−3x−6x2−4
=(3cancel((x-2))(x+1))/(cancel((x-2))(x+2))
=(3(x+1))/(x+2)
"with restriction "x!=-2
