Algebra Examples

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

Step 1

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = \frac{6}{2 (- 3) - 3}$

Step 2

Simplify the result.

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Step 2.1

Cancel the common factor of $6$ and $2 (- 3) - 3$ .

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Step 2.1.1

Factor $3$ out of $6$ .

$f (- 3) = \frac{3 (2)}{2 (- 3) - 3}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $3$ out of $2 (- 3)$ .

$f (- 3) = \frac{3 (2)}{3 (2 \cdot (- 1)) - 3}$

Step 2.1.2.2

Factor $3$ out of $- 3$ .

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

Step 2.1.2.3

Factor $3$ out of $3 (2 \cdot (- 1)) + 3 (- 1)$ .

$f (- 3) = \frac{3 (2)}{3 (2 \cdot (- 1) - 1)}$

Step 2.1.2.4

Cancel the common factor.

$f (- 3) = \frac{3 \cdot 2}{3 (2 \cdot (- 1) - 1)}$

Step 2.1.2.5

Rewrite the expression.

$f (- 3) = \frac{2}{2 \cdot (- 1) - 1}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $2$ by $- 1$ .

$f (- 3) = \frac{2}{- 2 - 1}$

Step 2.2.2

Subtract $1$ from $- 2$ .

$f (- 3) = \frac{2}{- 3}$

Step 2.3

Move the negative in front of the fraction.

$f (- 3) = - \frac{2}{3}$

Step 2.4

The final answer is $- \frac{2}{3}$ .

$- \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$

Step 4