Question 196762
# 1


{{{(6x*sqrt(3)-18x*sqrt(2))/(3x*sqrt(3)-27x)}}} Start with the given expression.



{{{(6x(sqrt(3)-3*sqrt(2)))/(3x*sqrt(3)-27x)}}} Factor out the GCF {{{6x}}} from the numerator.



{{{(6x(sqrt(3)-3*sqrt(2)))/(3x(sqrt(3)-9))}}} Factor out the GCF {{{3x}}} from the denominator.



{{{(3x*2(sqrt(3)-3*sqrt(2)))/(3x(sqrt(3)-9))}}} Factor {{{6x}}} into {{{3x*2}}}



{{{(highlight(3x)*2(sqrt(3)-3*sqrt(2)))/(highlight(3x)(sqrt(3)-9))}}} Highlight the common terms. 



{{{(cross(3x)*2(sqrt(3)-3*sqrt(2)))/(cross(3x)(sqrt(3)-9))}}} Cancel out the common terms. 




{{{(2(sqrt(3)-3*sqrt(2)))/(sqrt(3)-9)}}} Simplify



{{{(2*sqrt(3)-6*sqrt(2))/(sqrt(3)-9)}}} Distribute



So 

{{{(6x*sqrt(3)-18x*sqrt(2))/(3x*sqrt(3)-27x)}}} simplifies to {{{(2*sqrt(3)-6*sqrt(2))/(sqrt(3)-9)}}}



In other words, {{{(6x*sqrt(3)-18x*sqrt(2))/(3x*sqrt(3)-27x)=(2*sqrt(3)-6*sqrt(2))/(sqrt(3)-9)}}} where {{{x<>0}}}



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# 2





{{{(3x-15)/(4x-20)}}} Start with the given expression.



{{{(3(x-5))/(4x-20)}}} Factor {{{3x-15}}} to get {{{3(x-5)}}}.



{{{(3(x-5))/(4(x-5))}}} Factor {{{4x-20}}} to get {{{4(x-5)}}}.



{{{(3*highlight((x-5)))/(4*highlight((x-5)))}}} Highlight the common terms. 



{{{(3*cross((x-5)))/(4*cross((x-5)))}}} Cancel out the common terms. 



{{{3/4}}} Simplify. 



So {{{(3x-15)/(4x-20)}}} simplifies to {{{3/4}}}.



In other words, {{{(3x-15)/(4x-20)=3/4}}} where {{{x<>5}}}.