Question 155256
I'll do the first two to get you started


# 1


{{{(y^2-y-12)/(y^2-9)}}} Start with the given expression



{{{((y+3)(y-4))/(y^2-9)}}} Factor the numerator 



{{{((y+3)(y-4))/((y+3)(y-3))}}} Factor the denominator 



{{{(highlight((y+3))(y-4))/(highlight((y+3))(y-3))}}} Highlight the common terms



{{{(cross((y+3))(y-4))/(cross((y+3))(y-3))}}} Cancel out the common terms



{{{(y-4)/(y-3)}}} Simplify



So {{{(y^2-y-12)/(y^2-9)}}} simplifies to {{{(y-4)/(y-3)}}}



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# 2


Are you sure that the denominator is not {{{2x^2-8x-64}}}?



{{{(3x^2-6x-72)/(2x^2-8x-64)}}} Start with the given expression



{{{(3(x-6)(x+4))/(2x^2-8x-64)}}} Factor the numerator 



{{{(3(x-6)(x+4))/(2(x-8)(x+4))}}} Factor the denominator 



{{{(3(x-6)highlight((x+4)))/(2(x-8)highlight((x+4)))}}} Highlight the common terms



{{{(3(x-6)cross((x+4)))/(2(x-8)cross((x+4)))}}}  Cancel out the common terms



{{{(3(x-6))/(2(x-8))}}} Simplify



{{{(3x-18)/(2x-16)}}} Distribute



So {{{(3x^2-6x-72)/(2x^2-8x-64)}}} simplifies to {{{(3x-18)/(2x-16)}}}