Question 236422

{{{((x^2-x-72)/(x^2-x-30))/((x^2+6x-27)/(x^2-9x+18))}}} Start with the given expression.



{{{((x^2-x-72)/(x^2-x-30))((x^2-9x+18)/(x^2+6x-27))}}} Multiply the first fraction {{{(x^2-x-72)/(x^2-x-30)}}} by the reciprocal of the second fraction {{{(x^2+6x-27)/(x^2-9x+18)}}}.



{{{(((x+8)*(x-9))/(x^2-x-30))((x^2-9x+18)/(x^2+6x-27))}}} Factor {{{x^2-x-72}}} to get {{{(x+8)*(x-9)}}}.



{{{(((x+8)*(x-9))/((x+5)*(x-6)))((x^2-9x+18)/(x^2+6x-27))}}} Factor {{{x^2-x-30}}} to get {{{(x+5)*(x-6)}}}.



{{{(((x+8)*(x-9))/((x+5)*(x-6)))(((x-3)*(x-6))/(x^2+6x-27))}}} Factor {{{x^2-9x+18}}} to get {{{(x-3)*(x-6)}}}.



{{{(((x+8)*(x-9))/((x+5)*(x-6)))(((x-3)*(x-6))/((x+9)*(x-3)))}}} Factor {{{x^2+6x-27}}} to get {{{(x+9)*(x-3)}}}.



{{{((x+8)*(x-9)(x-3)*(x-6))/((x+5)*(x-6)(x+9)*(x-3))}}} Combine the fractions. 



{{{((x+8)(x-9)highlight((x-3))highlight((x-6)))/((x+5)highlight((x-6))(x+9)highlight((x-3)))}}} Highlight the common terms. 



{{{((x+8)(x-9)cross((x-3))cross((x-6)))/((x+5)cross((x-6))(x+9)cross((x-3)))}}} Cancel out the common terms. 



{{{((x+8)(x-9))/((x+5)(x+9))}}} Simplify. 



{{{(x^2-x-72)/(x^2+14x+45)}}} FOIL



So {{{((x^2-x-72)/(x^2-x-30))/((x^2+6x-27)/(x^2-9x+18))}}} simplifies to {{{(x^2-x-72)/(x^2+14x+45)}}}.



In other words, {{{((x^2-x-72)/(x^2-x-30))/((x^2+6x-27)/(x^2-9x+18))=(x^2-x-72)/(x^2+14x+45)}}}