Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $x^{2}$ and $x^{2}$ .

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

Step 3

Add $- 2 x$ and $x$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Factor $x$ out of $- x$ .

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

Step 4.3

Factor $x$ out of $x (2 x) + x \cdot - 1$ .

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

Step 5

Factor $x$ out of $x^{2} + 3 x$ .

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Step 5.1

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

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

Step 5.2

Factor $x$ out of $3 x$ .

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

Step 5.3

Factor $x$ out of $x \cdot x + x \cdot 3$ .

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

Step 6

Cancel the common factor of $x$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{2 x - 1}{x + 3}$