Question 125840
{{{((-12+2w)/5)/((49w-294)/25)}}} Start with the given expression


{{{((-12+2w)/5)*((25)/(49w-294))}}} Multiply the first fraction by the reciprocal of the second fraction



{{{((2(w-6))/(5))((25)/(49w-294))}}}   Factor {{{-12+2w}}} to get {{{2(-6+w)}}} and rearrange the inner terms to get {{{2(w-6)}}} 



{{{((2(w-6))/(5))((5*5)/(49w-294))}}}   Factor {{{25}}} to get {{{5*5}}} 


{{{((2(w-6))/(5))((5*5)/(49(w-6)))}}}   Factor {{{49w-294}}} to get {{{49(w-6)}}} 



{{{2(w-6)(5*5)/5(49(w-6))}}} Combine the fractions



{{{2cross((w-6))(cross(5)*5)/cross(5)(49cross((w-6)))}}} Cancel like terms



{{{(2*5)/49}}} Simplify



{{{10/49}}} Multiply




So {{{((-12+2w)/5)/((49w-294)/25)}}} simplifies to {{{10/49}}} 



In other words, {{{((-12+2w)/5)/((49w-294)/25)=10/49}}}