Question 196958

{{{((5y)/(5y+15))/((15y)/(y+3))}}} Start with the given expression.



{{{((5y)/(5y+15))((y+3)/(15y))}}} Multiply the first fraction {{{(5y)/(5y+15)}}} by the reciprocal of the second fraction {{{(15y)/(y+3)}}}.



{{{((5y)/(5(y+3)))((y+3)/(15y))}}} Factor {{{5y+15}}} to get {{{5(y+3)}}}.



{{{((5y)/(5(y+3)))(((y+3))/(3*5y))}}} Factor {{{15y}}} to get {{{3*5y}}}.



{{{(5y(y+3))/(5*3*5y(y+3))}}} Combine the fractions. 



{{{(highlight(5y)highlight((y+3)))/(5*3*highlight(5y)highlight((y+3)))}}} Highlight the common terms. 



{{{(cross(5y)cross((y+3)))/(5*3*cross(5y)cross((y+3)))}}} Cancel out the common terms. 



{{{1/(5*3)}}} Simplify. 



{{{1/15}}} Multiply



So {{{((5y)/(5y+15))/((15y)/(y+3))}}} simplifies to {{{1/15}}}.



In other words, {{{((5y)/(5y+15))/((15y)/(y+3))=1/15}}} where {{{y<>-3}}} or {{{y<>0}}}