Simplify ((x^2-2x)/(x^2+3x-10))÷((x-5)/(x+5))

$\frac{x^{2} - 2 x}{x^{2} + 3 x - 10} \div \frac{x - 5}{x + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

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

Factor $x$ out of $- 2 x$ .

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

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

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

Step 3

Factor $x^{2} + 3 x - 10$ 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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Write the factored form using these integers.

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

Step 4

Simplify terms.

Cancel the common factor of $x + 5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((x^2-2x)/(x^2+3x-10))÷((x-5)/(x+5))

Related Questions

Support LCMGCF.com by disabling your adblocker.