Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Raise $x$ to the power of $1$ .

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

Step 1.3

Factor $x$ out of $x^{1}$ .

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

Step 1.4

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

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

Step 2

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

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Step 2.1

Multiply $\frac{x + 4}{x - 1}$ by $\frac{x (x + 1)}{x - 1}$ .

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

Step 2.2

Raise $x - 1$ to the power of $1$ .

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

Step 2.3

Raise $x - 1$ to the power of $1$ .

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

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.5

Add $1$ and $1$ .

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

Step 3

Reorder factors in $\frac{(x + 4) x (x + 1)}{{(x - 1)}^{2}}$ .

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