Pre-Algebra Examples

$\frac{7 x}{x^{2} - 5 x} + \frac{x^{2}}{x - 5}$

Step 1

Simplify each term.

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Step 1.1

Factor $x$ out of $x^{2} - 5 x$ .

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Step 1.1.1

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

$\frac{7 x}{x \cdot x - 5 x} + \frac{x^{2}}{x - 5}$

Step 1.1.2

Factor $x$ out of $- 5 x$ .

$\frac{7 x}{x \cdot x + x \cdot - 5} + \frac{x^{2}}{x - 5}$

Step 1.1.3

Factor $x$ out of $x \cdot x + x \cdot - 5$ .

$\frac{7 x}{x (x - 5)} + \frac{x^{2}}{x - 5}$

Step 1.2

Cancel the common factor of $x$ .

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Step 1.2.1

Cancel the common factor.

$\frac{7 x}{x (x - 5)} + \frac{x^{2}}{x - 5}$

Step 1.2.2

Rewrite the expression.

$\frac{7}{x - 5} + \frac{x^{2}}{x - 5}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 + x^{2}}{x - 5}$