Precalculus Examples

$\frac{21}{x - 5} - \frac{13}{x^{2} - 5 x}$

Step 1

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

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Step 1.1

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

$\frac{21}{x - 5} - \frac{13}{x \cdot x - 5 x}$

Step 1.2

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

$\frac{21}{x - 5} - \frac{13}{x \cdot x + x \cdot - 5}$

Step 1.3

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

$\frac{21}{x - 5} - \frac{13}{x (x - 5)}$

Step 2

To write $\frac{21}{x - 5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{21}{x - 5} \cdot \frac{x}{x} - \frac{13}{x (x - 5)}$

Step 3

Write each expression with a common denominator of $(x - 5) x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{21}{x - 5}$ by $\frac{x}{x}$ .

$\frac{21 x}{(x - 5) x} - \frac{13}{x (x - 5)}$

Step 3.2

Reorder the factors of $(x - 5) x$ .

$\frac{21 x}{x (x - 5)} - \frac{13}{x (x - 5)}$

Step 4

Combine the numerators over the common denominator.

$\frac{21 x - 13}{x (x - 5)}$