Question 151700
{{{((d^2)/(d+4))/((d^2-4d)/(d^2+8d+16))}}} Start with the given expression.



{{{((d^2)/(d+4))((d^2+8d+16)/(d^2-4d))}}} Multiply the first fraction {{{(d^2)/(d+4)}}} by the reciprocal of the second fraction {{{(d^2-4d)/(d^2+8d+16)}}}.



{{{((d*d)/(d+4))((d^2+8d+16)/(d^2-4d))}}} Factor {{{d^2}}} to get {{{d*d}}}.



{{{((d*d)/(d+4))(((d+4)(d+4))/(d^2-4d))}}} Factor {{{d^2+8d+16}}} to get {{{(d+4)(d+4)}}}.



{{{((d*d)/(d+4))(((d+4)(d+4))/(d*(d-4)))}}} Factor {{{d^2-4d}}} to get {{{d*(d-4)}}}.



{{{(d*d(d+4)(d+4))/(d(d+4)(d-4))}}} Combine the fractions. 



{{{(highlight(d)*d*highlight((d+4))(d+4))/(highlight(d)highlight((d+4))(d-4))}}} Highlight the common terms. 



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



{{{(d(d+4))/(d-4)}}} Simplify. 



{{{(d^2+4d)/(d-4)}}} Distribute. 



So {{{((d^2)/(d+4))/((d^2-4d)/(d^2+8d+16))}}} simplifies to {{{(d^2+4d)/(d-4)}}}.



In other words, {{{((d^2)/(d+4))/((d^2-4d)/(d^2+8d+16))=(d^2+4d)/(d-4)}}} where {{{d<>0}}}, {{{d<>-4}}}, or {{{d<>4}}}