### Home > PC3 > Chapter 3 > Lesson 3.2.2 > Problem3-109

3-109.

Simplify each of the following expressions.

1. $\left(1+\frac{x}{y}\right)\left(\frac{4y^2}{x^2-y^2}\right)$

Rewrite the first factor as a single fraction. Do this by rewriting $1$ as $\frac{y}{y}$.

$\large \left(\frac{y+x}{y}\right)\left(\frac{4y^2}{x^2-y^2}\right)$

1. $\large \frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } - 16 } \div \frac { x ^ { 2 } - 4 x + 4 } { x + 4 }$

Since you are dividing, invert the second fraction and multiply.
Be sure to factor all of the expressions and then simplify.

1. $\left( \frac { x ^ { - 2 } + x ^ { - 1 } } { x + x ^ { - 3 } } \right) ^ { - 1 }$

$\large \left(\frac{x+x^{-3}}{x^{-2}+x^{-1}}\right)^1$

$\large \frac{x+\frac{1}{x^3}}{\frac{1}{x^2}+\frac{1}{x}}$

$\large \left(\frac{x+\frac{1}{x^3}}{\frac{1}{x^2}+\frac{1}{x}}\right)\left(\frac{\frac{x^3}{1}}{\frac{x^3}{1}}\right)$