Simplify ((x^2-1)/(2x+2))÷((x^2-6x+5)/(2x^2))

$\frac{x^{2} - 1}{2 x + 2} \div \frac{x^{2} - 6 x + 5}{2 x^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 1}{2 x + 2} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

$\frac{x^{2} - 1^{2}}{2 x + 2} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

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 $b = 1$ .

$\frac{(x + 1) (x - 1)}{2 x + 2} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Simplify terms.

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

Factor $2$ out of $2 x$ .

$\frac{(x + 1) (x - 1)}{2 (x) + 2} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Factor $2$ out of $2$ .

$\frac{(x + 1) (x - 1)}{2 (x) + 2 (1)} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Factor $2$ out of $2 (x) + 2 (1)$ .

$\frac{(x + 1) (x - 1)}{2 (x + 1)} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Cancel the common factor of $2$ .

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

$\frac{(x + 1) (x - 1)}{2 (x + 1)} \cdot \frac{2 (x^{2})}{x^{2} - 6 x + 5}$

Cancel the common factor.

$\frac{(x + 1) (x - 1)}{2 (x + 1)} \cdot \frac{2 x^{2}}{x^{2} - 6 x + 5}$

Rewrite the expression.

$\frac{(x + 1) (x - 1)}{x + 1} \cdot \frac{x^{2}}{x^{2} - 6 x + 5}$

Multiply $\frac{(x + 1) (x - 1)}{x + 1}$ by $\frac{x^{2}}{x^{2} - 6 x + 5}$ .

$\frac{(x + 1) (x - 1) x^{2}}{(x + 1) (x^{2} - 6 x + 5)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x + 1) (x - 1) x^{2}}{(x + 1) (x^{2} - 6 x + 5)}$

Rewrite the expression.

$\frac{(x - 1) x^{2}}{x^{2} - 6 x + 5}$

Factor $x^{2} - 6 x + 5$ 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 $5$ and whose sum is $- 6$ .

$- 5, - 1$

Write the factored form using these integers.

$\frac{(x - 1) x^{2}}{(x - 5) (x - 1)}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x - 1) x^{2}}{(x - 5) (x - 1)}$

Rewrite the expression.

$\frac{x^{2}}{x - 5}$

Simplify ((x^2-1)/(2x+2))÷((x^2-6x+5)/(2x^2))

Related Questions

Support LCMGCF.com by disabling your adblocker.