Calculus Examples

$- \frac{x (y + 3) (y - 3)}{(x + 2) (x - 2)} = 0$

Step 1

Set the numerator equal to zero.

$x (y + 3) (y - 3) = 0$

Step 2

Divide each term in $x (y + 3) (y - 3) = 0$ by $(y + 3) (y - 3)$ and simplify.

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Step 2.1

Divide each term in $x (y + 3) (y - 3) = 0$ by $(y + 3) (y - 3)$ .

$\frac{x (y + 3) (y - 3)}{(y + 3) (y - 3)} = \frac{0}{(y + 3) (y - 3)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $y + 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x (y + 3) (y - 3)}{(y + 3) (y - 3)} = \frac{0}{(y + 3) (y - 3)}$

Step 2.2.1.2

Rewrite the expression.

$\frac{x (y - 3)}{y - 3} = \frac{0}{(y + 3) (y - 3)}$

Step 2.2.2

Cancel the common factor of $y - 3$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{x (y - 3)}{y - 3} = \frac{0}{(y + 3) (y - 3)}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{0}{(y + 3) (y - 3)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $(y + 3) (y - 3)$ .

$x = 0$

Step 3

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = 0$