Simplify (2x^2+16x+30)/(5x^2+13x-6)

$\frac{2 x^{2} + 16 x + 30}{5 x^{2} + 13 x - 6}$

Step 1

Simplify the numerator.

Factor $2$ out of $2 x^{2} + 16 x + 30$ .

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x^{2}) + 16 x + 30}{5 x^{2} + 13 x - 6}$

Factor $2$ out of $16 x$ .

$\frac{2 (x^{2}) + 2 (8 x) + 30}{5 x^{2} + 13 x - 6}$

Factor $2$ out of $30$ .

$\frac{2 x^{2} + 2 (8 x) + 2 \cdot 15}{5 x^{2} + 13 x - 6}$

Factor $2$ out of $2 x^{2} + 2 (8 x)$ .

$\frac{2 (x^{2} + 8 x) + 2 \cdot 15}{5 x^{2} + 13 x - 6}$

Factor $2$ out of $2 (x^{2} + 8 x) + 2 \cdot 15$ .

$\frac{2 (x^{2} + 8 x + 15)}{5 x^{2} + 13 x - 6}$

Factor $x^{2} + 8 x + 15$ using the AC method.

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 $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$\frac{2 ((x + 3) (x + 5))}{5 x^{2} + 13 x - 6}$

$\frac{2 (x + 3) (x + 5)}{5 x^{2} + 13 x - 6}$

Step 2

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 $a \cdot c = 5 \cdot - 6 = - 30$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$\frac{2 (x + 3) (x + 5)}{5 x^{2} + 13 (x) - 6}$

Rewrite $13$ as $- 2$ plus $15$

$\frac{2 (x + 3) (x + 5)}{5 x^{2} + (- 2 + 15) x - 6}$

Apply the distributive property.

$\frac{2 (x + 3) (x + 5)}{5 x^{2} - 2 x + 15 x - 6}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 (x + 3) (x + 5)}{(5 x^{2} - 2 x) + 15 x - 6}$

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

$\frac{2 (x + 3) (x + 5)}{x (5 x - 2) + 3 (5 x - 2)}$

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

$\frac{2 (x + 3) (x + 5)}{(5 x - 2) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{2 (x + 3) (x + 5)}{(5 x - 2) (x + 3)}$

Rewrite the expression.

$\frac{2 (x + 5)}{5 x - 2}$

Simplify (2x^2+16x+30)/(5x^2+13x-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.