Answer
Part A:
$\frac{y}{xy + 1}$
Part B:
$\frac{1}{x^{4}}$
Work Step by Step
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:
$\frac{y}{x^{4}y}$ = $\frac{1}{x^{4}}$
