Basic Math Examples

\frac{- 8 c + 14 d}{6 c} - \frac{10 c - 7 d}{6 c}

$\frac{- 8 c + 14 d}{6 c} - \frac{10 c - 7 d}{6 c}$

Step 1

Combine the numerators over the common denominator.

\frac{- 8 c + 14 d - (10 c - 7 d)}{6 c}

$\frac{- 8 c + 14 d - (10 c - 7 d)}{6 c}$

Step 2

Rewrite

\frac{- 8 c + 14 d - (10 c - 7 d)}{6 c}

$\frac{- 8 c + 14 d - (10 c - 7 d)}{6 c}$ in a factored form.

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Step 2.1

Factor

- 1

$- 1$ out of

- 8 c + 14 d - (10 c - 7 d)

$- 8 c + 14 d - (10 c - 7 d)$ .

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Step 2.1.1

Reorder the expression.

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Step 2.1.1.1

Move

14 d

$14 d$ .

\frac{- 8 c - (10 c - 7 d) + 14 d}{6 c}

$\frac{- 8 c - (10 c - 7 d) + 14 d}{6 c}$

Step 2.1.1.2

Reorder

- 8 c

$- 8 c$ and

- (10 c - 7 d)

$- (10 c - 7 d)$ .

\frac{- (10 c - 7 d) - 8 c + 14 d}{6 c}

$\frac{- (10 c - 7 d) - 8 c + 14 d}{6 c}$

\frac{- (10 c - 7 d) - 8 c + 14 d}{6 c}

$\frac{- (10 c - 7 d) - 8 c + 14 d}{6 c}$

Step 2.1.2

Factor

- 1

$- 1$ out of

- 8 c

$- 8 c$ .

\frac{- (10 c - 7 d) - (8 c) + 14 d}{6 c}

$\frac{- (10 c - 7 d) - (8 c) + 14 d}{6 c}$

Step 2.1.3

Factor

- 1

$- 1$ out of

14 d

$14 d$ .

\frac{- (10 c - 7 d) - (8 c) - (- 14 d)}{6 c}

$\frac{- (10 c - 7 d) - (8 c) - (- 14 d)}{6 c}$

Step 2.1.4

Factor

- 1

$- 1$ out of

- (10 c - 7 d) - (8 c)

$- (10 c - 7 d) - (8 c)$ .

\frac{- (10 c - 7 d + 8 c) - (- 14 d)}{6 c}

$\frac{- (10 c - 7 d + 8 c) - (- 14 d)}{6 c}$

Step 2.1.5

Factor

- 1

$- 1$ out of

- (10 c - 7 d + 8 c) - (- 14 d)

$- (10 c - 7 d + 8 c) - (- 14 d)$ .

\frac{- (10 c - 7 d + 8 c - 14 d)}{6 c}

$\frac{- (10 c - 7 d + 8 c - 14 d)}{6 c}$

\frac{- (10 c - 7 d + 8 c - 14 d)}{6 c}

$\frac{- (10 c - 7 d + 8 c - 14 d)}{6 c}$

Step 2.2

Add

10 c

$10 c$ and

8 c

$8 c$ .

\frac{- (18 c - 7 d - 14 d)}{6 c}

$\frac{- (18 c - 7 d - 14 d)}{6 c}$

Step 2.3

Subtract

14 d

$14 d$ from

- 7 d

$- 7 d$ .

\frac{- (18 c - 21 d)}{6 c}

$\frac{- (18 c - 21 d)}{6 c}$

Step 2.4

Factor.

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Step 2.4.1

Factor

3

$3$ out of

18 c - 21 d

$18 c - 21 d$ .

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Step 2.4.1.1

Factor

3

$3$ out of

18 c

$18 c$ .

\frac{- (3 (6 c) - 21 d)}{6 c}

$\frac{- (3 (6 c) - 21 d)}{6 c}$

Step 2.4.1.2

Factor

3

$3$ out of

- 21 d

$- 21 d$ .

\frac{- (3 (6 c) + 3 (- 7 d))}{6 c}

$\frac{- (3 (6 c) + 3 (- 7 d))}{6 c}$

Step 2.4.1.3

Factor

3

$3$ out of

3 (6 c) + 3 (- 7 d)

$3 (6 c) + 3 (- 7 d)$ .

\frac{- (3 (6 c - 7 d))}{6 c}

$\frac{- (3 (6 c - 7 d))}{6 c}$

\frac{- (3 (6 c - 7 d))}{6 c}

$\frac{- (3 (6 c - 7 d))}{6 c}$

Step 2.4.2

Remove unnecessary parentheses.

\frac{- 1 \cdot 3 (6 c - 7 d)}{6 c}

$\frac{- 1 \cdot 3 (6 c - 7 d)}{6 c}$

\frac{- 1 \cdot 3 (6 c - 7 d)}{6 c}

$\frac{- 1 \cdot 3 (6 c - 7 d)}{6 c}$

Step 2.5

Multiply

- 1

$- 1$ by

3

$3$ .

$\frac{- 3 (6 c - 7 d)}{6 c}$

Step 2.6

Reduce the expression

$\frac{- 3 (6 c - 7 d)}{6 c}$ by cancelling the common factors.

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Step 2.6.1

Factor

$3$ out of

$- 3 (6 c - 7 d)$ .

$\frac{3 (- (6 c - 7 d))}{6 c}$

Step 2.6.2

Factor

$3$ out of

$6 c$ .

$\frac{3 (- (6 c - 7 d))}{3 (2 c)}$

Step 2.6.3

Cancel the common factor.

$\frac{3 (- (6 c - 7 d))}{3 (2 c)}$

Step 2.6.4

Rewrite the expression.

$\frac{- (6 c - 7 d)}{2 c}$