How do you simplify #\frac { x ^ { 2} - 2x - 8} { x ^ { 3} + x ^ { 2} - 2x }#?

1 Answer
Jim G.
Jul 29, 2017

#(x-4)/(x(x-1))#

Explanation:

#"factorise numerator/denominator and cancel any "#
#color(blue)"common factors"#

#"numerator"#

#x^2-2x-8#

#=(x-4)(x+2)#

#"denominator"#

#x^3+x^2-2x#

#=x(x^2+x-2)#

#=x(x+2)(x-1)#

#rArr(x^2-2x-8)/(x^3+x^2-2x)#

#=((x-4)cancel((x+2)))/(xcancel((x+2))(x-1))#

#=(x-4)/(x(x-1))to(x!=0,x!=1)#

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