Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $x - 1$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 4

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

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