### Home > PC > Chapter 4 > Lesson 4.1.2 > Problem4-30

4-30.

Given $x^2 + y^2 = 1$, simplify each of the following expressions.

1. $\frac { 1 } { y } - y$

Write with one common denominator.
$\frac{1-y^2}{y}$

Substitute $y^2$ with $1 − x^2$ from the given equation.
$\frac{1-(1-x^2)}{y}$

Simplify.
$\frac{x^2}{y}$

1. $\frac { x } { y } + \frac { y } { x }$

Rewrite the expression with a common denominator.
Substitute from the given equation.

1. $\frac { x - \frac { 1 } { x } } { \frac { y } { x } }$

Rewrite the expression in the numerator with a common denominator.
Simplify and substitute.

1. $( \frac { 1 } { x } - x ) ( y - \frac { 1 } { y } )$

1. Multiply out.
2. Make all fractions with the same common denominator.
3. Simplify.