Question 307063
Factor the polynomials and look for identical factors to cancel out.
{{{x^2+2x-15=(x+5)(x-3)}}}
{{{x^2-x-30=(x-6)(x+5)}}}
{{{x^2-3x-18=(x-6)(x+3)}}}
{{{x^2-2x-24=(x-6)(x+4)}}}
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{{{(x^2+2x-15)/(x^2-x-30)=((x+5)(x-3))/((x-6)(x+5))}}}
{{{(x^2+2x-15)/(x^2-x-30)=(cross(x+5)(x-3))/((x-6)cross(x+5))}}}
{{{(x^2+2x-15)/(x^2-x-30)= (x-3)/(x-6)}}}
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{{{(x^2-3x-18)/(x^2-2x-24) =((x-6)(x+3))/((x-6)(x+4))}}}
{{{(x^2-3x-18)/(x^2-2x-24)=(cross(x-6)(x+3))/(cross(x-6)(x+4))}}}
{{{(x^2-3x-18)/(x^2-2x-24)= (x+3)/(x+4)}}}
Dividing by a fraction is like multiplying by its reciprocal
{{{((x^2+2x-15)/(x^2-x-30))/((x^2-3x-18)/(x^2-2x-24))=((x-3)/(x-6))/((x+3)/(x+4))}}}
{{{((x^2+2x-15)/(x^2-x-30))/((x^2-3x-18)/(x^2-2x-24))=((x-3)/(x-6))*((x+4)/(x+3))}}}