Basic Math Examples

$\frac{16 y^{2} - 49}{y^{2} - 4} \div \frac{4 y + 7}{y + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{16 y^{2} - 49}{y^{2} - 4} \cdot \frac{y + 2}{4 y + 7}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

$\frac{{(4 y)}^{2} - 49}{y^{2} - 4} \cdot \frac{y + 2}{4 y + 7}$

Step 2.2

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

$\frac{{(4 y)}^{2} - 7^{2}}{y^{2} - 4} \cdot \frac{y + 2}{4 y + 7}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 y$ and $b = 7$ .

$\frac{(4 y + 7) (4 y - 7)}{y^{2} - 4} \cdot \frac{y + 2}{4 y + 7}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $4$ as $2^{2}$ .

$\frac{(4 y + 7) (4 y - 7)}{y^{2} - 2^{2}} \cdot \frac{y + 2}{4 y + 7}$

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 $a = y$ and $b = 2$ .

$\frac{(4 y + 7) (4 y - 7)}{(y + 2) (y - 2)} \cdot \frac{y + 2}{4 y + 7}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of $4 y + 7$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

$\frac{(4 y + 7) (4 y - 7)}{(y + 2) (y - 2)} \cdot \frac{y + 2}{4 y + 7}$

Step 4.1.2

Rewrite the expression.

$\frac{4 y - 7}{(y + 2) (y - 2)} (y + 2)$

Step 4.2

Cancel the common factor of $y + 2$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{4 y - 7}{(y + 2) (y - 2)} (y + 2)$

Step 4.2.2

Rewrite the expression.

$\frac{4 y - 7}{y - 2}$