Question 203584


{{{((6s^2+st-2t^2)/(6s^2-5st+t^2))/((3s^2+17st+10t^2)/(6s^2+13st-5t^2))}}} Start with the given expression.



{{{((6s^2+st-2t^2)/(6s^2-5st+t^2))((6s^2+13st-5t^2)/(3s^2+17st+10t^2))}}} Multiply the first fraction {{{(6s^2+st-2t^2)/(6s^2-5st+t^2)}}} by the reciprocal of the second fraction {{{(3s^2+17st+10t^2)/(6s^2+13st-5t^2)}}}.



{{{(((3s+2t)(2s-t))/(6s^2-5st+t^2))((6s^2+13st-5t^2)/(3s^2+17st+10t^2))}}} Factor {{{6s^2+st-2t^2}}} to get {{{(3s+2t)(2s-t)}}}.



{{{(((3s+2t)(2s-t))/((3s-t)(2s-t)))((6s^2+13st-5t^2)/(3s^2+17st+10t^2))}}} Factor {{{6s^2-5st+t^2}}} to get {{{(3s-t)(2s-t)}}}.



{{{(((3s+2t)(2s-t))/((3s-t)(2s-t)))(((2s+5t)(3s-t))/(3s^2+17st+10t^2))}}} Factor {{{6s^2+13st-5t^2}}} to get {{{(2s+5t)(3s-t)}}}.



{{{(((3s+2t)(2s-t))/((3s-t)(2s-t)))(((2s+5t)(3s-t))/((s+5t)(3s+2t)))}}} Factor {{{3s^2+17st+10t^2}}} to get {{{(s+5t)(3s+2t)}}}.



{{{((3s+2t)(2s-t)(2s+5t)(3s-t))/((3s-t)(2s-t)(s+5t)(3s+2t))}}} Combine the fractions. 



{{{(highlight((3s+2t))highlight((2s-t))(2s+5t)highlight((3s-t)))/(highlight((3s-t))highlight((2s-t))(s+5t)highlight((3s+2t)))}}} Highlight the common terms. 



{{{(cross((3s+2t))cross((2s-t))(2s+5t)cross((3s-t)))/(cross((3s-t))cross((2s-t))(s+5t)cross((3s+2t)))}}} Cancel out the common terms. 



{{{(2s+5t)/(s+5t)}}} Simplify. 



So {{{((6s^2+st-2t^2)/(6s^2-5st+t^2))/((3s^2+17st+10t^2)/(6s^2+13st-5t^2))}}} simplifies to {{{(2s+5t)/(s+5t)}}}.



In other words, {{{((6s^2+st-2t^2)/(6s^2-5st+t^2))/((3s^2+17st+10t^2)/(6s^2+13st-5t^2))=(2s+5t)/(s+5t)}}}