Basic Math Examples

$\frac{\frac{1}{j - 9}}{\frac{3}{j^{2} - 81}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{j - 9} \cdot \frac{j^{2} - 81}{3}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $81$ as $9^{2}$ .

$\frac{1}{j - 9} \cdot \frac{j^{2} - 9^{2}}{3}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = j$ and $b = 9$ .

$\frac{1}{j - 9} \cdot \frac{(j + 9) (j - 9)}{3}$

Step 3

Cancel the common factor of $j - 9$ .

Tap for more steps...

Step 3.1

Factor $j - 9$ out of $(j + 9) (j - 9)$ .

$\frac{1}{j - 9} \cdot \frac{(j - 9) (j + 9)}{3}$

Step 3.2

Cancel the common factor.

$\frac{1}{j - 9} \cdot \frac{(j - 9) (j + 9)}{3}$

Step 3.3

Rewrite the expression.

$\frac{j + 9}{3}$