Simplify (2m+6)/(3m^2+11m+6)

$\frac{2 m + 6}{3 m^{2} + 11 m + 6}$

Step 1

Factor $2$ out of $2 m + 6$ .

Factor $2$ out of $2 m$ .

$\frac{2 (m) + 6}{3 m^{2} + 11 m + 6}$

Factor $2$ out of $6$ .

$\frac{2 m + 2 \cdot 3}{3 m^{2} + 11 m + 6}$

Factor $2$ out of $2 m + 2 \cdot 3$ .

$\frac{2 (m + 3)}{3 m^{2} + 11 m + 6}$

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 $a \cdot c = 3 \cdot 6 = 18$ and whose sum is $b = 11$ .

Factor $11$ out of $11 m$ .

$\frac{2 (m + 3)}{3 m^{2} + 11 (m) + 6}$

Rewrite $11$ as $2$ plus $9$

$\frac{2 (m + 3)}{3 m^{2} + (2 + 9) m + 6}$

Apply the distributive property.

$\frac{2 (m + 3)}{3 m^{2} + 2 m + 9 m + 6}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 (m + 3)}{(3 m^{2} + 2 m) + 9 m + 6}$

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

$\frac{2 (m + 3)}{m (3 m + 2) + 3 (3 m + 2)}$

Factor the polynomial by factoring out the greatest common factor, $3 m + 2$ .

$\frac{2 (m + 3)}{(3 m + 2) (m + 3)}$

Step 3

Cancel the common factor of $m + 3$ .

Cancel the common factor.

$\frac{2 (m + 3)}{(3 m + 2) (m + 3)}$

Rewrite the expression.

$\frac{2}{3 m + 2}$

Simplify (2m+6)/(3m^2+11m+6)

Related Questions