Basic Math Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

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

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Step 2.1

Factor $- 1$ out of $- 8 c + 14 d - (10 c - 7 d)$ .

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Step 2.1.1

Reorder the expression.

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Step 2.1.1.1

Move $14 d$ .

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

Step 2.1.1.2

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

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

Step 2.1.2

Factor $- 1$ out of $- 8 c$ .

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

Step 2.1.3

Factor $- 1$ out of $14 d$ .

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

Step 2.1.4

Factor $- 1$ out of $- (10 c - 7 d) - (8 c)$ .

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

Step 2.1.5

Factor $- 1$ out of $- (10 c - 7 d + 8 c) - (- 14 d)$ .

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

Step 2.2

Add $10 c$ and $8 c$ .

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

Step 2.3

Subtract $14 d$ from $- 7 d$ .

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

Step 2.4

Factor.

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Step 2.4.1

Factor $3$ out of $18 c - 21 d$ .

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Step 2.4.1.1

Factor $3$ out of $18 c$ .

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

Step 2.4.1.2

Factor $3$ out of $- 21 d$ .

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

Step 2.4.1.3

Factor $3$ out of $3 (6 c) + 3 (- 7 d)$ .

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

Step 2.4.2

Remove unnecessary parentheses.

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

Step 2.5

Multiply $- 1$ by $3$ .

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

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.

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