Basic Math Examples

$\frac{\frac{21 a^{3}}{49 - a^{2}}}{\frac{3 a^{2}}{7 - a}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{21 a^{3}}{49 - a^{2}} \cdot \frac{7 - a}{3 a^{2}}$

Step 2

Cancel the common factor of $3 a^{2}$ .

Tap for more steps...

Step 2.1

Factor $3 a^{2}$ out of $21 a^{3}$ .

$\frac{3 a^{2} (7 a)}{49 - a^{2}} \cdot \frac{7 - a}{3 a^{2}}$

Step 2.2

Cancel the common factor.

$\frac{3 a^{2} (7 a)}{49 - a^{2}} \cdot \frac{7 - a}{3 a^{2}}$

Step 2.3

Rewrite the expression.

$\frac{7 a}{49 - a^{2}} (7 - a)$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $49$ as $7^{2}$ .

$\frac{7 a}{7^{2} - a^{2}} (7 - a)$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7$ and $b = a$ .

$\frac{7 a}{(7 + a) (7 - a)} (7 - a)$

Step 4

Cancel the common factor of $7 - a$ .

Tap for more steps...

Step 4.1

Factor $7 - a$ out of $(7 + a) (7 - a)$ .

$\frac{7 a}{(7 - a) (7 + a)} (7 - a)$

Step 4.2

Cancel the common factor.

$\frac{7 a}{(7 - a) (7 + a)} (7 - a)$

Step 4.3

Rewrite the expression.

$\frac{7 a}{7 + a}$