Basic Math Examples

$\frac{3 c + 4}{3} + \frac{12 - 8 c}{6}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $12 - 8 c$ and $6$ .

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Step 1.1.1

Factor $2$ out of $12$ .

$\frac{3 c + 4}{3} + \frac{2 (6) - 8 c}{6}$

Step 1.1.2

Factor $2$ out of $- 8 c$ .

$\frac{3 c + 4}{3} + \frac{2 (6) + 2 (- 4 c)}{6}$

Step 1.1.3

Factor $2$ out of $2 (6) + 2 (- 4 c)$ .

$\frac{3 c + 4}{3} + \frac{2 (6 - 4 c)}{6}$

Step 1.1.4

Cancel the common factors.

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Step 1.1.4.1

Factor $2$ out of $6$ .

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

Step 1.1.4.2

Cancel the common factor.

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

Step 1.1.4.3

Rewrite the expression.

$\frac{3 c + 4}{3} + \frac{6 - 4 c}{3}$

$\frac{3 c + 4}{3} + \frac{6 - 4 c}{3}$

$\frac{3 c + 4}{3} + \frac{6 - 4 c}{3}$

Step 1.2

Factor $2$ out of $6 - 4 c$ .

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Step 1.2.1

Factor $2$ out of $6$ .

$\frac{3 c + 4}{3} + \frac{2 (3) - 4 c}{3}$

Step 1.2.2

Factor $2$ out of $- 4 c$ .

$\frac{3 c + 4}{3} + \frac{2 (3) + 2 (- 2 c)}{3}$

Step 1.2.3

Factor $2$ out of $2 (3) + 2 (- 2 c)$ .

$\frac{3 c + 4}{3} + \frac{2 (3 - 2 c)}{3}$

$\frac{3 c + 4}{3} + \frac{2 (3 - 2 c)}{3}$

$\frac{3 c + 4}{3} + \frac{2 (3 - 2 c)}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 c + 4 + 2 (3 - 2 c)}{3}$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$\frac{3 c + 4 + 2 \cdot 3 + 2 (- 2 c)}{3}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{3 c + 4 + 6 + 2 (- 2 c)}{3}$

Step 3.3

Multiply $- 2$ by $2$ .

$\frac{3 c + 4 + 6 - 4 c}{3}$

$\frac{3 c + 4 + 6 - 4 c}{3}$

Step 4

Simplify terms.

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Step 4.1

Subtract $4 c$ from $3 c$ .

$\frac{- c + 4 + 6}{3}$

Step 4.2

Add $4$ and $6$ .

$\frac{- c + 10}{3}$

Step 4.3

Factor $- 1$ out of $- c$ .

$\frac{- (c) + 10}{3}$

Step 4.4

Rewrite $10$ as $- 1 (- 10)$ .

$\frac{- (c) - 1 (- 10)}{3}$

Step 4.5

Factor $- 1$ out of $- (c) - 1 (- 10)$ .

$\frac{- (c - 10)}{3}$

Step 4.6

Simplify the expression.

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Step 4.6.1

Rewrite $- (c - 10)$ as $- 1 (c - 10)$ .

$\frac{- 1 (c - 10)}{3}$

Step 4.6.2

Move the negative in front of the fraction.

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

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

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

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