CPM Homework Help : PCT Problem 4-30

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4-30.

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

$\frac { 1 } { y } - y$
Step 1(a):
Write with one common denominator.
$\frac{1-y^2}{y}$
Step 2(a):
Substitute $y^2$ with $1 − x^2$ from the given equation.
$\frac{1-(1-x^2)}{y}$
Step 3(a):
Simplify.
$\frac{x^2}{y}$

$\frac { x } { y } + \frac { y } { x }$
Hint (b):
Rewrite the expression with a common denominator.
Substitute from the given equation.

$\frac { x - \frac { 1 } { x } } { \frac { y } { x } }$
Hint (c):
Rewrite the expression in the numerator with a common denominator.
Simplify and substitute.

$( \frac { 1 } { x } - x ) ( y - \frac { 1 } { y } )$
Hint (d):
1. Multiply out.
2. Make all fractions with the same common denominator.
3. Simplify.

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