How do you simplify (x^2+21x+90)/(x^2+17x+66) + (2x^2+17x+21)/(2x^2+25x+33)?

1 Answer
Oct 20, 2015

(x^2+21x+90)/(x^2+17x+66)+(2x^2+17x+21)/(2x^2+25x+33)=2

Explanation:

First, factor all quadratic expressions.

[1]color(white)(XX)(x^2+21x+90)/(x^2+17x+66)+(2x^2+17x+21)/(2x^2+25x+33)

[2]color(white)(XX)=[(x+6)(x+15)]/[(x+6)(x+11)]+[(2x+3)(x+7)]/[(2x+3)(x+11)]

Cancel any common factors.

[3]color(white)(XX)=[cancel((x+6))(x+15)]/[cancel((x+6))(x+11)]+[cancel((2x+3))(x+7)]/[cancel((2x+3))(x+11)]

[4]color(white)(XX)=(x+15)/(x+11)+(x+7)/(x+11)

Add the two together.

[5]color(white)(XX)=[(x+15)+(x+7)]/(x+11)

[6]color(white)(XX)=(2x+22)/(x+11)

Factor out 2 from 2x+22.

[7]color(white)(XX)=(2(x+11))/(x+11)

Cancel out the common factor.

[8]color(white)(XX)=(2cancel((x+11)))/cancel((x+11))

[8]color(white)(XX)=color(red)(2)