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

Oct 20, 2015

$\frac{{x}^{2} + 21 x + 90}{{x}^{2} + 17 x + 66} + \frac{2 {x}^{2} + 17 x + 21}{2 {x}^{2} + 25 x + 33} = 2$

#### Explanation:

$\left[1\right] \textcolor{w h i t e}{X X} \frac{{x}^{2} + 21 x + 90}{{x}^{2} + 17 x + 66} + \frac{2 {x}^{2} + 17 x + 21}{2 {x}^{2} + 25 x + 33}$

$\left[2\right] \textcolor{w h i t e}{X X} = \frac{\left(x + 6\right) \left(x + 15\right)}{\left(x + 6\right) \left(x + 11\right)} + \frac{\left(2 x + 3\right) \left(x + 7\right)}{\left(2 x + 3\right) \left(x + 11\right)}$

Cancel any common factors.

$\left[3\right] \textcolor{w h i t e}{X X} = \frac{\cancel{\left(x + 6\right)} \left(x + 15\right)}{\cancel{\left(x + 6\right)} \left(x + 11\right)} + \frac{\cancel{\left(2 x + 3\right)} \left(x + 7\right)}{\cancel{\left(2 x + 3\right)} \left(x + 11\right)}$

$\left[4\right] \textcolor{w h i t e}{X X} = \frac{x + 15}{x + 11} + \frac{x + 7}{x + 11}$

$\left[5\right] \textcolor{w h i t e}{X X} = \frac{\left(x + 15\right) + \left(x + 7\right)}{x + 11}$

$\left[6\right] \textcolor{w h i t e}{X X} = \frac{2 x + 22}{x + 11}$

Factor out 2 from $2 x + 22$.

$\left[7\right] \textcolor{w h i t e}{X X} = \frac{2 \left(x + 11\right)}{x + 11}$

Cancel out the common factor.

$\left[8\right] \textcolor{w h i t e}{X X} = \frac{2 \cancel{\left(x + 11\right)}}{\cancel{\left(x + 11\right)}}$

$\left[8\right] \textcolor{w h i t e}{X X} = \textcolor{red}{2}$