Question 119844
{{{((2x-6)/21)/((5x-15)/12)}}} Start with the given expression


{{{((2x-6)/(21))((12)/(5x-15))}}} Multiply the first fraction by the reciprocal of the second


{{{((2(x-3))/(21))((12)/(5x-15))}}}   Factor {{{2x-6}}} to get {{{2(x-3)}}} 


{{{((2(x-3))/(3*7))((12)/(5x-15))}}}   Factor {{{21}}} to get {{{3*7}}} 


{{{((2(x-3))/(3*7))((3*4)/(5x-15))}}}   Factor {{{12}}} to get {{{3*4}}} 


{{{((2(x-3))/(3*7))((3*4)/(5(x-3)))}}}   Factor {{{5x-15}}} to get {{{5(x-3)}}} 



{{{2(x-3)(3*4)/(3*7*5(x-3))}}} Combine the fractions



{{{2cross((x-3))(cross(3)*4)/(cross(3)*7*5cross((x-3)))}}} Combine the fractions




{{{(2*4)/(7*5)}}} Cancel like terms




{{{8/35}}} Multiply




So {{{((2x-6)/21)/((5x-15)/12)}}} simplifies to {{{8/35}}}



In other words, {{{((2x-6)/21)/((5x-15)/12)=8/35}}}