Algebra Examples

$\frac{z^{3} - 4 z^{2} + 2 z}{z^{2} - 5 z + 6}$ , $z = - 3$

Step 1

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

$\frac{{(- 3)}^{3} - 4 {(- 3)}^{2} + 2 (- 3)}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{- 27 - 4 {(- 3)}^{2} + 2 (- 3)}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2.2

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

$\frac{- 27 - 4 \cdot 9 + 2 (- 3)}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2.3

Multiply $- 4$ by $9$ .

$\frac{- 27 - 36 + 2 (- 3)}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2.4

Multiply $2$ by $- 3$ .

$\frac{- 27 - 36 - 6}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2.5

Subtract $36$ from $- 27$ .

$\frac{- 63 - 6}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 2.6

Subtract $6$ from $- 63$ .

$\frac{- 69}{{(- 3)}^{2} - 5 \cdot - 3 + 6}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{- 69}{9 - 5 \cdot - 3 + 6}$

Step 3.2

Multiply $- 5$ by $- 3$ .

$\frac{- 69}{9 + 15 + 6}$

Step 3.3

Add $9$ and $15$ .

$\frac{- 69}{24 + 6}$

Step 3.4

Add $24$ and $6$ .

$\frac{- 69}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 69$ and $30$ .

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Step 4.1.1

Factor $3$ out of $- 69$ .

$\frac{3 (- 23)}{30}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $3$ out of $30$ .

$\frac{3 \cdot - 23}{3 \cdot 10}$

Step 4.1.2.2

Cancel the common factor.

$\frac{3 \cdot - 23}{3 \cdot 10}$

Step 4.1.2.3

Rewrite the expression.

$\frac{- 23}{10}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{23}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{10}$

Decimal Form:

$- 2.3$

Mixed Number Form:

$- 2 \frac{3}{10}$