Pre-Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $2 x$ and $3 x$ .

$\frac{5 x + 2 + 3}{x^{2} + x}$

Step 3

Add $2$ and $3$ .

$\frac{5 x + 5}{x^{2} + x}$

Step 4

Factor $5$ out of $5 x + 5$ .

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Step 4.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 5}{x^{2} + x}$

Step 4.2

Factor $5$ out of $5$ .

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

Step 4.3

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

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

$\frac{5 (x + 1)}{x (x + 1)}$

Step 6

Cancel the common factor of $x + 1$ .

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Step 6.1

Cancel the common factor.

$\frac{5 (x + 1)}{x (x + 1)}$

Step 6.2

Rewrite the expression.

$\frac{5}{x}$