Simplify (x-6)/(5x)*(x^2-49)/(x^2+x-42)

$\frac{x - 6}{5 x} \cdot \frac{x^{2} - 49}{x^{2} + x - 42}$

Step 1

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$\frac{x - 6}{5 x} \cdot \frac{x^{2} - 7^{2}}{x^{2} + x - 42}$

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 $b = 7$ .

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

Step 2

Factor $x^{2} + x - 42$ 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 $- 42$ and whose sum is $1$ .

$- 6, 7$

Write the factored form using these integers.

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

Step 3

Simplify terms.

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5 x} \cdot \frac{(x + 7) (x - 7)}{x + 7}$

Multiply $\frac{1}{5 x}$ by $\frac{(x + 7) (x - 7)}{x + 7}$ .

$\frac{(x + 7) (x - 7)}{5 x (x + 7)}$

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{(x + 7) (x - 7)}{5 x (x + 7)}$

Rewrite the expression.

$\frac{x - 7}{5 x}$

Simplify (x-6)/(5x)*(x^2-49)/(x^2+x-42)

Related Questions

Support LCMGCF.com by disabling your adblocker.