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

1 Answer
Mar 14, 2018

Answer:

#(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#