Simplify (2x+6)/(5x+10)*(x+2)/(x^2+4x+3)

$\frac{2 x + 6}{5 x + 10} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Step 1

Simplify with factoring out.

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

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 6}{5 x + 10} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Factor $2$ out of $6$ .

$\frac{2 x + 2 \cdot 3}{5 x + 10} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

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

$\frac{2 (x + 3)}{5 x + 10} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Factor $5$ out of $5 x + 10$ .

Factor $5$ out of $5 x$ .

$\frac{2 (x + 3)}{5 (x) + 10} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Factor $5$ out of $10$ .

$\frac{2 (x + 3)}{5 x + 5 \cdot 2} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Factor $5$ out of $5 x + 5 \cdot 2$ .

$\frac{2 (x + 3)}{5 (x + 2)} \cdot \frac{x + 2}{x^{2} + 4 x + 3}$

Step 2

Factor $x^{2} + 4 x + 3$ 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 $3$ and whose sum is $4$ .

$1, 3$

Write the factored form using these integers.

$\frac{2 (x + 3)}{5 (x + 2)} \cdot \frac{x + 2}{(x + 1) (x + 3)}$

Step 3

Simplify terms.

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of $2 (x + 3)$ .

$\frac{(x + 3) \cdot 2}{5 (x + 2)} \cdot \frac{x + 2}{(x + 1) (x + 3)}$

Factor $x + 3$ out of $(x + 1) (x + 3)$ .

$\frac{(x + 3) \cdot 2}{5 (x + 2)} \cdot \frac{x + 2}{(x + 3) (x + 1)}$

Cancel the common factor.

$\frac{(x + 3) \cdot 2}{5 (x + 2)} \cdot \frac{x + 2}{(x + 3) (x + 1)}$

Rewrite the expression.

$\frac{2}{5 (x + 2)} \cdot \frac{x + 2}{x + 1}$

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $5 (x + 2)$ .

$\frac{2}{(x + 2) \cdot 5} \cdot \frac{x + 2}{x + 1}$

Cancel the common factor.

$\frac{2}{(x + 2) \cdot 5} \cdot \frac{x + 2}{x + 1}$

Rewrite the expression.

$\frac{2}{5} \cdot \frac{1}{x + 1}$

Multiply $\frac{2}{5}$ by $\frac{1}{x + 1}$ .

$\frac{2}{5 (x + 1)}$

Simplify (2x+6)/(5x+10)*(x+2)/(x^2+4x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.