How do you simplify #(3x^2-3x-6)/(x^2-4)#?
1 Answer
May 12, 2018
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#