How do you simplify #(2x^2+x-15)/(2x^2-11x-21)*(6x+9)div(2x-5)/(3x-21)#?

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Answer 1 · 2017-04-20T05:59:35

#9(x+3)#

Given: #(2x^2+x-15)/(2x^2-11x-21) * (6x+9) -: (2x-5)/(3x-21)#

Change the division problem to multiplication by reciprocating the last rational function:

#(2x^2+x-15)/(2x^2-11x-21) * (6x+9) * (3x-21)/(2x-5)#

Make the second polynomial a fraction:

#(2x^2+x-15)/(2x^2-11x-21) * (6x+9)/1 * (3x-21)/(2x-5)#

Factor each polynomial:

#((x+3)(2x-5))/((2x+3)(x-7)) * (3(2x+3))/1 * (3(x-7))/(2x-5)#

Cancel all factors that occur in both the numerator & denominator:

#(color(red)(x+3)cancel(2x-5))/(cancel(2x+3)cancel(x-7)) * (color(red)(3)cancel(2x+3))/1 * (color(red)(3)cancel(x-7))/(cancel(2x-5))#

#= 9(x+3)#