Simplify (y^2-36)/(5y^2-26y-24)

$\frac{y^{2} - 36}{5 y^{2} - 26 y - 24}$

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{y^{2} - 6^{2}}{5 y^{2} - 26 y - 24}$

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 $b = 6$ .

$\frac{(y + 6) (y - 6)}{5 y^{2} - 26 y - 24}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot - 24 = - 120$ and whose sum is $b = - 26$ .

Factor $- 26$ out of $- 26 y$ .

$\frac{(y + 6) (y - 6)}{5 y^{2} - 26 (y) - 24}$

Rewrite $- 26$ as $4$ plus $- 30$

$\frac{(y + 6) (y - 6)}{5 y^{2} + (4 - 30) y - 24}$

Apply the distributive property.

$\frac{(y + 6) (y - 6)}{5 y^{2} + 4 y - 30 y - 24}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(y + 6) (y - 6)}{(5 y^{2} + 4 y) - 30 y - 24}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(y + 6) (y - 6)}{y (5 y + 4) - 6 (5 y + 4)}$

Factor the polynomial by factoring out the greatest common factor, $5 y + 4$ .

$\frac{(y + 6) (y - 6)}{(5 y + 4) (y - 6)}$

Cancel the common factor of $y - 6$ .

Cancel the common factor.

$\frac{(y + 6) (y - 6)}{(5 y + 4) (y - 6)}$

Rewrite the expression.

$\frac{y + 6}{5 y + 4}$

Simplify (y^2-36)/(5y^2-26y-24)

Related Questions

Support LCMGCF.com by disabling your adblocker.