How do you solve this?

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2 Answers
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.

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