Linear Algebra Examples

$\frac{1 (- 3)}{x} - \frac{18}{x^{2}}$

Step 1

Multiply $1$ by $- 3$ .

$\frac{- 3}{x} - \frac{18}{x^{2}}$

Step 2

Move the negative in front of the fraction.

$- \frac{3}{x} - \frac{18}{x^{2}}$

Step 3

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- \frac{3}{x} \cdot \frac{x}{x} - \frac{18}{x^{2}}$

Step 4

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{x}$ by $\frac{x}{x}$ .

$- \frac{3 x}{x \cdot x} - \frac{18}{x^{2}}$

Step 4.2

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

$- \frac{3 x}{x^{1} x} - \frac{18}{x^{2}}$

Step 4.3

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

$- \frac{3 x}{x^{1} x^{1}} - \frac{18}{x^{2}}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{3 x}{x^{1 + 1}} - \frac{18}{x^{2}}$

Step 4.5

Add $1$ and $1$ .

$- \frac{3 x}{x^{2}} - \frac{18}{x^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 3 x - 18}{x^{2}}$

Step 6

Factor $3$ out of $- 3 x - 18$ .

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Step 6.1

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 18}{x^{2}}$

Step 6.2

Factor $3$ out of $- 18$ .

$\frac{3 (- x) + 3 (- 6)}{x^{2}}$

Step 6.3

Factor $3$ out of $3 (- x) + 3 (- 6)$ .

$\frac{3 (- x - 6)}{x^{2}}$

Step 7

Factor $- 1$ out of $- x$ .

$\frac{3 (- (x) - 6)}{x^{2}}$

Step 8

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{3 (- (x) - 1 (6))}{x^{2}}$

Step 9

Factor $- 1$ out of $- (x) - 1 (6)$ .

$\frac{3 (- (x + 6))}{x^{2}}$

Step 10

Simplify the expression.

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Step 10.1

Rewrite $- (x + 6)$ as $- 1 (x + 6)$ .

$\frac{3 (- 1 (x + 6))}{x^{2}}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{3 (x + 6)}{x^{2}}$