Linear Algebra Examples

$\frac{- 3^{2} - 10 \cdot - 3 + 5}{- 3^{2} + 2 (- 3) - 1}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{- 1 \cdot 9 - 10 \cdot - 3 + 5}{- 3^{2} + 2 (- 3) - 1}$

Step 1.2

Multiply $- 1$ by $9$ .

$\frac{- 9 - 10 \cdot - 3 + 5}{- 3^{2} + 2 (- 3) - 1}$

Step 1.3

Multiply $- 10$ by $- 3$ .

$\frac{- 9 + 30 + 5}{- 3^{2} + 2 (- 3) - 1}$

Step 1.4

Add $- 9$ and $30$ .

$\frac{21 + 5}{- 3^{2} + 2 (- 3) - 1}$

Step 1.5

Add $21$ and $5$ .

$\frac{26}{- 3^{2} + 2 (- 3) - 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{26}{- 1 \cdot 9 + 2 (- 3) - 1}$

Step 2.2

Multiply $- 1$ by $9$ .

$\frac{26}{- 9 + 2 (- 3) - 1}$

Step 2.3

Multiply $2$ by $- 3$ .

$\frac{26}{- 9 - 6 - 1}$

Step 2.4

Subtract $6$ from $- 9$ .

$\frac{26}{- 15 - 1}$

Step 2.5

Subtract $1$ from $- 15$ .

$\frac{26}{- 16}$

Step 3

Cancel the common factor of $26$ and $- 16$ .

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Step 3.1

Factor $2$ out of $26$ .

$\frac{2 (13)}{- 16}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $- 16$ .

$\frac{2 \cdot 13}{2 \cdot - 8}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \cdot 13}{2 \cdot - 8}$

Step 3.2.3

Rewrite the expression.

$\frac{13}{- 8}$

Step 4

Move the negative in front of the fraction.

$- \frac{13}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{8}$

Decimal Form:

$- 1.625$

Mixed Number Form:

$- 1 \frac{5}{8}$