Question 149578
# 1


{{{(18x^2+48x+32)/(3x+4)}}} Start with the given expression.



{{{(2(3x+4)(3x+4))/(3x+4)}}} Factor {{{18x^2+48x+32}}} to get {{{2(3x+4)(3x+4)}}}.



{{{(2highlight((3x+4))(3x+4))/highlight((3x+4))}}} Highlight the common terms. 



{{{(2cross((3x+4))(3x+4))/cross((3x+4))}}} Cancel out the common terms. 



{{{2(3x+4)}}} Simplify. 



{{{6x+8}}} Distribute



So {{{(18x^2+48x+32)/(3x+4)}}} simplifies to {{{6x+8}}}.



In other words, {{{(18x^2+48x+32)/(3x+4)=6x+8}}} where {{{x<>-4/3}}}



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# 2




{{{((x-2)/(x+2))/((x-2)/(5))}}} Start with the given expression.



{{{((x-2)/(x+2))((5)/(x-2))}}} Multiply the first fraction {{{(x-2)/(x+2)}}} by the reciprocal of the second fraction {{{(x-2)/(5)}}}.




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



{{{(5highlight(x-2))/((x+2)highlight(x-2))}}} Highlight the common terms. 



{{{(5cross(x-2))/((x+2)cross(x-2))}}} Cancel out the common terms. 



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



So {{{((x-2)/(x+2))/((x-2)/(5))}}} simplifies to {{{(5)/(x+2)}}}.



In other words, {{{((x-2)/(x+2))/((x-2)/(5))=(5)/(x+2)}}} where {{{x<>-2}}} or {{{x<>2}}}