Question 150924

{{{((x^2-5x-14)/(8))((4)/(x-7))}}} Start with the given expression.



{{{(((x+2)(x-7))/((2)(4)))((4)/(x-7))}}} Factor {{{x^2-5x-14}}} to get {{{(x+2)(x-7)}}}.



{{{(((x+2)(x-7))/((2)(4)))((4)/(x-7))}}} Factor {{{8}}} to get {{{(2)(4)}}}.



{{{((x+2)(x-7)(4))/((2)(4)(x-7))}}} Combine the fractions. 



{{{((x+2)highlight((x-7))highlight(4))/((2)highlight(4)highlight((x-7)))}}} Highlight the common terms. 



{{{((x+2)cross((x-7))cross(4))/((2)cross(4)cross((x-7)))}}} Cancel out the common terms. 



{{{(x+2)/(2)}}} Simplify. 



So {{{((x^2-5x-14)/(8))((4)/(x-7))}}} simplifies to {{{(x+2)/(2)}}}.



In other words, {{{((x^2-5x-14)/(8))((4)/(x-7))=(x+2)/(2)}}} where {{{x<>7}}}