Question 1199800
<pre>
simplify this algebraic fraction: (y^2-y-6)/(y^2-25) ÷ (3-y)/(5-y)
answer : (y+2)/(y+5)
how is this simplified ?

What did you try? I guess nothing!

{{{((y^2 - y - 6)/(y^2 - 25))/((3 - y)/(5 - y))}}} ====> {{{(y^2 - y - 6)/(y^2 - 25)}}} ÷ {{{(3 - y)/(5 - y)}}}

{{{((y - 3)(y + 2))/((y - 5)(y + 5))}}} ÷ {{{(3 - y)/(5 - y)}}} ----- Factoring 1st fraction's numerator and denominator

{{{((y - 3)(y + 2)/(y - 5)(y + 5)) * ((5 - y)/(3 - y))}}} ----- Applying KCF

{{{((y - 3)(y + 2)/((y - 5)(y + 5))) * ((- 1)(- 5 + y)/- 1(- 3 + y))}}} ---- Multiplying 2nd fraction's numerator and denominator by - 1 to
                                      match the factors in 1st fraction's numerator and denominator
{{{((y - 3)(y + 2)/((y - 5)(y + 5))) * ((- 1)(y - 5)/- 1(y - 3))}}} 

{{{matrix(1,3, (cross((y - 3))(y + 2)/(cross((y - 5))(y + 5))) * (cross((- 1))cross((y - 5))/cross(- 1)cross((y - 3))), "=",  highlight(highlight_green(highlight((y + 2)/(y + 5)))))}}}</pre>