Question 189442

{{{((x^2+18x+81)/(-28x))/((x+9)/(-7x))}}} Start with the given expression.



{{{((x^2+18x+81)/(-28x))((-7x)/(x+9))}}} Multiply the first fraction {{{(x^2+18x+81)/(-28x)}}} by the reciprocal of the second fraction {{{(x+9)/(-7x)}}}.



{{{(((x+9)(x+9))/(-28x))((-7x)/(x+9))}}} Factor {{{x^2+18x+81}}} to get {{{(x+9)(x+9)}}}.



{{{(((x+9)(x+9))/(-7x*4))((-7x)/(x+9))}}} Factor {{{-28x}}} to get {{{-7*4x}}}. Rearrange to get {{{-7x*4}}}



{{{(-7x(x+9)(x+9))/(-7x*4(x+9))}}} Combine the fractions. 



{{{(highlight(-7x)*highlight((x+9))(x+9))/(highlight(-7x)*4*highlight((x+9)))}}} Highlight the common terms. 



{{{(cross(-7x)*cross((x+9))(x+9))/(cross(-7x)*4*cross((x+9)))}}} Cancel out the common terms. 



{{{(x+9)/4}}} Simplify. 



So {{{((x^2+18x+81)/(-28x))/((x+9)/(-7x))}}} simplifies to {{{(x+9)/4}}}.



In other words, {{{((x^2+18x+81)/(-28x))/((x+9)/(-7x)) = (x+9)/4}}} where {{{x<>-9}}} or {{{x<>0}}}