Basic Math Examples

$\frac{\frac{y^{2} - 5 y - 6}{y^{2} - 49}}{\frac{y - 6}{y - 6}}$

Step 1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.1

Cancel the common factor of $y - 6$ .

Tap for more steps...

Step 1.1.1

Cancel the common factor.

$\frac{\frac{y^{2} - 5 y - 6}{y^{2} - 49}}{\frac{y - 6}{y - 6}}$

Step 1.1.2

Rewrite the expression.

$\frac{\frac{y^{2} - 5 y - 6}{y^{2} - 49}}{1}$

Step 1.2

Divide $\frac{y^{2} - 5 y - 6}{y^{2} - 49}$ by $1$ .

$\frac{y^{2} - 5 y - 6}{y^{2} - 49}$

Step 2

Factor $y^{2} - 5 y - 6$ using the AC method.

Tap for more steps...

Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 5$ .

$- 6, 1$

Step 2.2

Write the factored form using these integers.

$\frac{(y - 6) (y + 1)}{y^{2} - 49}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

$\frac{(y - 6) (y + 1)}{y^{2} - 7^{2}}$

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 $b = 7$ .

$\frac{(y - 6) (y + 1)}{(y + 7) (y - 7)}$