Simplify (2x+14)/(x^2-25)*(8x+40)/(6x+42)

$\frac{2 x + 14}{x^{2} - 25} \cdot \frac{8 x + 40}{6 x + 42}$

Factor $2$ out of $2 x + 14$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 14}{x^{2} - 25} \cdot \frac{8 x + 40}{6 x + 42}$

Factor $2$ out of $14$ .

$\frac{2 x + 2 \cdot 7}{x^{2} - 25} \cdot \frac{8 x + 40}{6 x + 42}$

Factor $2$ out of $2 x + 2 \cdot 7$ .

$\frac{2 (x + 7)}{x^{2} - 25} \cdot \frac{8 x + 40}{6 x + 42}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$\frac{2 (x + 7)}{x^{2} - 5^{2}} \cdot \frac{8 x + 40}{6 x + 42}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 x + 40}{6 x + 42}$

Simplify terms.

Factor $8$ out of $8 x + 40$ .

Factor $8$ out of $8 x$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x) + 40}{6 x + 42}$

Factor $8$ out of $40$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 x + 8 \cdot 5}{6 x + 42}$

Factor $8$ out of $8 x + 8 \cdot 5$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{6 x + 42}$

Factor $6$ out of $6 x + 42$ .

Factor $6$ out of $6 x$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{6 (x) + 42}$

Factor $6$ out of $42$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{6 x + 6 \cdot 7}$

Factor $6$ out of $6 x + 6 \cdot 7$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{6 (x + 7)}$

Cancel the common factor of $2 (x + 7)$ .

Factor $2 (x + 7)$ out of $6 (x + 7)$ .

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{2 (x + 7) (3)}$

Cancel the common factor.

$\frac{2 (x + 7)}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{2 (x + 7) \cdot 3}$

Rewrite the expression.

$\frac{1}{(x + 5) (x - 5)} \cdot \frac{8 (x + 5)}{3}$

Cancel the common factor of $x + 5$ .

Factor $x + 5$ out of $8 (x + 5)$ .

$\frac{1}{(x + 5) (x - 5)} \cdot \frac{(x + 5) \cdot 8}{3}$

Cancel the common factor.

$\frac{1}{(x + 5) (x - 5)} \cdot \frac{(x + 5) \cdot 8}{3}$

Rewrite the expression.

$\frac{1}{x - 5} \cdot \frac{8}{3}$

Multiply $\frac{1}{x - 5}$ by $\frac{8}{3}$ .

$\frac{8}{(x - 5) \cdot 3}$

Move $3$ to the left of $x - 5$ .

$\frac{8}{3 (x - 5)}$

Simplify (2x+14)/(x^2-25)*(8x+40)/(6x+42)

Related Questions

Support LCMGCF.com by disabling your adblocker.