Algebra Examples

$\frac{b}{6} - \frac{3 a - 2 b}{6}$

Step 1

Combine the numerators over the common denominator.

$\frac{b - (3 a - 2 b)}{6}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{b - (3 a) - (- 2 b)}{6}$

Step 2.2

Multiply $3$ by $- 1$ .

$\frac{b - 3 a - (- 2 b)}{6}$

Step 2.3

Multiply $- 2$ by $- 1$ .

$\frac{b - 3 a + 2 b}{6}$

$\frac{b - 3 a + 2 b}{6}$

Step 3

Simplify terms.

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Step 3.1

Add $b$ and $2 b$ .

$\frac{- 3 a + 3 b}{6}$

Step 3.2

Cancel the common factor of $- 3 a + 3 b$ and $6$ .

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Step 3.2.1

Factor $3$ out of $- 3 a$ .

$\frac{3 (- a) + 3 b}{6}$

Step 3.2.2

Factor $3$ out of $3 b$ .

$\frac{3 (- a) + 3 (b)}{6}$

Step 3.2.3

Factor $3$ out of $3 (- a) + 3 (b)$ .

$\frac{3 (- a + b)}{6}$

Step 3.2.4

Cancel the common factors.

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Step 3.2.4.1

Factor $3$ out of $6$ .

$\frac{3 (- a + b)}{3 (2)}$

Step 3.2.4.2

Cancel the common factor.

$\frac{3 (- a + b)}{3 \cdot 2}$

Step 3.2.4.3

Rewrite the expression.

$\frac{- a + b}{2}$

$\frac{- a + b}{2}$

$\frac{- a + b}{2}$

Step 3.3

Factor $- 1$ out of $- a$ .

$\frac{- (a) + b}{2}$

Step 3.4

Factor $- 1$ out of $b$ .

$\frac{- (a) - 1 (- b)}{2}$

Step 3.5

Factor $- 1$ out of $- (a) - 1 (- b)$ .

$\frac{- (a - b)}{2}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite $- (a - b)$ as $- 1 (a - b)$ .

$\frac{- 1 (a - b)}{2}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{a - b}{2}$

$- \frac{a - b}{2}$

$- \frac{a - b}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$