Question 170421
{{{((8p - 8)/p)/((10p - 10)/(6p^2))}}} Start with the given expression




{{{((8p - 8)/p)*((6p^2)/(10p - 10))}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{((8(p-1))/p)*((6p^2)/(10p - 10))}}} Factor  {{{8p - 8}}} to get {{{8(p-1)}}}



{{{((8(p-1))/p)*((2*3*p*p)/(10p - 10))}}} Factor  {{{6p^2}}} to get {{{2*3*p*p}}}



{{{((8(p-1))/p)*((2*3*p*p)/(2*5(p-1)))}}} Factor  {{{10p - 10}}} to get {{{10(p-1)=2*5(p-1)}}}



{{{(8(p-1))(2*3*p*p)/(2*5p(p-1))}}} Combine the fractions.



{{{(8*highlight((p-1)))(highlight(2)*3*highlight(p)*p)/(highlight(2)*5*highlight(p)*highlight((p-1)))}}} Highlight the common terms.



{{{(8*cross((p-1)))(cross(2)*3*cross(p)*p)/(cross(2)*5*cross(p)*cross((p-1)))}}} Cancel out the common terms.




{{{(8*3p)/(5)}}} Simplify



{{{(24p)/(5)}}} Multiply




So {{{((8p - 8)/p)/((10p - 10)/(6p^2))}}} simplifies to {{{(24p)/(5)}}}



In other words, {{{((8p - 8)/p)/((10p - 10)/(6p^2))=(24p)/(5)}}} where {{{p<>0}}} or {{{p<>-1}}}