Algebra Examples

$\frac{2 x^{2} - x - 24}{12 - 2 x}$ , $x = - 3$

Step 1

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

$\frac{2 {(- 3)}^{2} - (- 3) - 24}{12 - 2 \cdot - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $- 3$ to the power of $2$ .

$\frac{2 \cdot 9 - (- 3) - 24}{12 - 2 \cdot - 3}$

Step 2.2

Multiply $2$ by $9$ .

$\frac{18 - (- 3) - 24}{12 - 2 \cdot - 3}$

Step 2.3

Multiply $- 1$ by $- 3$ .

$\frac{18 + 3 - 24}{12 - 2 \cdot - 3}$

Step 2.4

Add $18$ and $3$ .

$\frac{21 - 24}{12 - 2 \cdot - 3}$

Step 2.5

Subtract $24$ from $21$ .

$\frac{- 3}{12 - 2 \cdot - 3}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $- 2$ by $- 3$ .

$\frac{- 3}{12 + 6}$

Step 3.2

Add $12$ and $6$ .

$\frac{- 3}{18}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 3$ and $18$ .

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Step 4.1.1

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{18}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $3$ out of $18$ .

$\frac{3 \cdot - 1}{3 \cdot 6}$

Step 4.1.2.2

Cancel the common factor.

$\frac{3 \cdot - 1}{3 \cdot 6}$

Step 4.1.2.3

Rewrite the expression.

$\frac{- 1}{6}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{6}$

Decimal Form:

$- 0.1\overline{6}$