Algebra Examples

$\frac{x^{2}}{x + 5} \cdot \frac{x^{2} + 4 x - 5}{x^{2} - 4 x}$

Step 1

Factor $x^{2} + 4 x - 5$ using the AC method.

Tap for more steps...

Step 1.1

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 $4$ .

$- 1, 5$

Step 1.2

Write the factored form using these integers.

$\frac{x^{2}}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x^{2} - 4 x}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $x$ out of $x^{2} - 4 x$ .

Tap for more steps...

Step 2.1.1

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

$\frac{x^{2}}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x \cdot x - 4 x}$

Step 2.1.2

Factor $x$ out of $- 4 x$ .

$\frac{x^{2}}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x \cdot x + x \cdot - 4}$

Step 2.1.3

Factor $x$ out of $x \cdot x + x \cdot - 4$ .

$\frac{x^{2}}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x (x - 4)}$

Step 2.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1

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

$\frac{x \cdot x}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x (x - 4)}$

Step 2.2.2

Cancel the common factor.

$\frac{x \cdot x}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x (x - 4)}$

Step 2.2.3

Rewrite the expression.

$\frac{x}{x + 5} \cdot \frac{(x - 1) (x + 5)}{x - 4}$

Step 2.3

Cancel the common factor of $x + 5$ .

Tap for more steps...

Step 2.3.1

Factor $x + 5$ out of $(x - 1) (x + 5)$ .

$\frac{x}{x + 5} \cdot \frac{(x + 5) (x - 1)}{x - 4}$

Step 2.3.2

Cancel the common factor.

$\frac{x}{x + 5} \cdot \frac{(x + 5) (x - 1)}{x - 4}$

Step 2.3.3

Rewrite the expression.

$x \cdot \frac{x - 1}{x - 4}$

Step 2.4

Combine $x$ and $\frac{x - 1}{x - 4}$ .

$\frac{x (x - 1)}{x - 4}$