Algebra Examples

$A = \frac{- 2 (9 - 3) - 3 (- 2 + 4)}{6 - (5 - 3)} + \frac{3}{2}$

Step 1

Simplify the expression.

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Step 1.1

Subtract $3$ from $9$ .

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

Step 1.2

Add $- 2$ and $4$ .

$A = \frac{- 2 \cdot 6 - 3 \cdot 2}{6 - (5 - 3)} + \frac{3}{2}$

Step 1.3

Multiply $- 2$ by $6$ .

$A = \frac{- 12 - 3 \cdot 2}{6 - (5 - 3)} + \frac{3}{2}$

Step 1.4

Multiply $- 3$ by $2$ .

$A = \frac{- 12 - 6}{6 - (5 - 3)} + \frac{3}{2}$

Step 1.5

Subtract $6$ from $- 12$ .

$A = \frac{- 18}{6 - (5 - 3)} + \frac{3}{2}$

Step 2

Simplify each term.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Subtract $3$ from $5$ .

$A = \frac{- 18}{6 - 1 \cdot 2} + \frac{3}{2}$

Step 2.1.2

Multiply $- 1$ by $2$ .

$A = \frac{- 18}{6 - 2} + \frac{3}{2}$

Step 2.1.3

Subtract $2$ from $6$ .

$A = \frac{- 18}{4} + \frac{3}{2}$

Step 2.2

Cancel the common factor of $- 18$ and $4$ .

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Step 2.2.1

Factor $2$ out of $- 18$ .

$A = \frac{2 (- 9)}{4} + \frac{3}{2}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $4$ .

$A = \frac{2 \cdot - 9}{2 \cdot 2} + \frac{3}{2}$

Step 2.2.2.2

Cancel the common factor.

$A = \frac{2 \cdot - 9}{2 \cdot 2} + \frac{3}{2}$

Step 2.2.2.3

Rewrite the expression.

$A = \frac{- 9}{2} + \frac{3}{2}$

Step 2.3

Move the negative in front of the fraction.

$A = - \frac{9}{2} + \frac{3}{2}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$A = \frac{- 9 + 3}{2}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Add $- 9$ and $3$ .

$A = \frac{- 6}{2}$

Step 3.2.2

Divide $- 6$ by $2$ .

$A = - 3$