How do you solve this?

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2 Answers
Aviv S.
Feb 22, 2018

The simplified expression is #11x+1#.

Explanation:

First, use factor by grouping on the numerator (basically FOIL but backward). We need to find two numbers that multiply to #-99# and add to #-2#. Those two numbers are #-11# and #9#, so:

#color(white)=(99q^2-2q-1)/(9q-1)#

#=(99q^2-11q+9q-1)/(9q-1)#

#=(11q(9q-1)+1(9q-1))/(9q-1)#

#=((11q+1)(9q-1))/(9q-1)#

#=((11q+1)color(red)cancel(color(black)((9q-1))))/color(red)cancel(color(black)((9q-1)))#

#=11q+1#

That's the simplified expression. You can verify that this answer is correct by graphing #(99x^2-2x-1)/(9x-1)# and also #11x+1# and see that they are the same graph.

Crater M.
Feb 22, 2018

#11q+1#

Explanation:

#(99q^2)/(9q-1)=11q+1 2/9+11/(81q-9)#

#(-2q)/(9q-1)=-2/9-2/(81q-9)#

#(-1)/(9q-1)=-9/(81q-9)#

#11q+1 2/9-2/9+11/(81q-9)-9/(81q-9)-2/(81q-9)#

#11q+1#

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