Question 150928

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



{{{((x^2-5x-14)/(8))((x-7)/(4))}}} Multiply the first fraction {{{(x^2-5x-14)/(8)}}} by the reciprocal of the second fraction {{{(4)/(x-7)}}}.



{{{(((x+2)*(x-7))/(8))((x-7)/(4))}}} Factor {{{x^2-5x-14}}} to get {{{(x+2)*(x-7)}}}.



{{{((x+2)(x-7)(x-7))/((8)(4))}}} Combine the fractions. 



{{{((x+2)(x-7)^2)/(32)}}} Multiply and simplify 



So {{{((x^2-5x-14)/(8))/((4)/(x-7))}}} simplifies to {{{((x+2)(x-7)^2)/(32)}}}.



In other words, {{{((x^2-5x-14)/(8))/((4)/(x-7))=((x+2)(x-7)^2)/(32)}}} where {{{x<>7}}}