## Algebra and Trigonometry 10th Edition

Part A: $\frac{y}{xy + 1}$ Part B: $\frac{1}{x^{4}}$
Note: $a^{n}a^{m} = a^{n + m}$ Note: $\frac{a^{n}}{a^{m}}$ = $a^{n-m}$ Note: $a^{0} = 1$ Part A: The problem can be rewritten as: $\frac{1}{x + \frac{1}{y}}$ A common denominator is needed to add fractions: $\frac{1}{\frac{xy}{y} + \frac{1}{y}}$ = $\frac{1}{\frac{xy + 1}{y}}$ That can be simplified using basic division rules to get: $\frac{y}{xy + 1}$ Part B: Using the second note the problem can be rewritten as $(\frac{1}{x^{3}y})(\frac{y}{x})$ Multiplying the two fractions gives: $\frac{y}{x^{4}y}$ = $\frac{1}{x^{4}}$