Simplify ((x+2)/(x^2+2x-3))/((x+2)/(x^2-x))

$\frac{\frac{x + 2}{x^{2} + 2 x - 3}}{\frac{x + 2}{x^{2} - x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x^{2} + 2 x - 3} (x^{2} - x)$

Step 3

Factor $x^{2} + 2 x - 3$ 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 $2$ .

$- 1, 3$

Write the factored form using these integers.

$\frac{1}{(x - 1) (x + 3)} (x^{2} - x)$

Step 4

Simplify terms.

Multiply $\frac{1}{(x - 1) (x + 3)}$ by $x^{2} - x$ .

$\frac{x^{2} - x}{(x - 1) (x + 3)}$

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

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

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{x + 3}$

Simplify ((x+2)/(x^2+2x-3))/((x+2)/(x^2-x))

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