Question 319697
Is the expression {{{((2(x-1)^2)/y)/(2/((x-1)y^4))}}} ????



{{{((2(x-1)^2)/y)/(2/((x-1)y^4))}}} Start with the given expression.



{{{((2(x-1)^2)/y)*(((x-1)y^4)/2)}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{(2y^4*(x-1)^2(x-1))/(2y)}}} Combine the fractions.



{{{(2y*y^3*(x-1)^2(x-1))/(2y)}}} Factor {{{2y^4}}} to get {{{2y*y^3}}}



{{{(highlight(2y)*y^3*(x-1)^2(x-1))/highlight(2y)}}} Highlight the common terms.



{{{(cross(2y)*y^3*(x-1)^2(x-1))/cross(2y)}}} Cancel out the common terms.



{{{y^3*(x-1)^2(x-1)}}} Simplify



{{{y^3*(x-1)^3}}} Multiply {{{(x-1)^2}}} and {{{x-1}}} to get {{{(x-1)^3}}}



So {{{((2(x-1)^2)/y)/(2/((x-1)y^4))=y^3*(x-1)^3}}}