Basic Math Examples

- \frac{8 a - 7 d}{8 a} - \frac{8 a + 10 d}{8 a}

$- \frac{8 a - 7 d}{8 a} - \frac{8 a + 10 d}{8 a}$

Step 1

Combine the numerators over the common denominator.

$\frac{- (8 a - 7 d) - (8 a + 10 d)}{8 a}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{- (8 a) - (- 7 d) - (8 a + 10 d)}{8 a}$

Step 2.2

Multiply

$8$ by

$- 1$ .

$\frac{- 8 a - (- 7 d) - (8 a + 10 d)}{8 a}$

Step 2.3

Multiply

$- 7$ by

$- 1$ .

$\frac{- 8 a + 7 d - (8 a + 10 d)}{8 a}$

Step 2.4

Apply the distributive property.

$\frac{- 8 a + 7 d - (8 a) - (10 d)}{8 a}$

Step 2.5

Multiply

$8$ by

$- 1$ .

$\frac{- 8 a + 7 d - 8 a - (10 d)}{8 a}$

Step 2.6

Multiply

$10$ by

$- 1$ .

$\frac{- 8 a + 7 d - 8 a - 10 d}{8 a}$

$\frac{- 8 a + 7 d - 8 a - 10 d}{8 a}$

Step 3

Simplify terms.

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Step 3.1

Subtract

$8 a$ from

$- 8 a$ .

$\frac{- 16 a + 7 d - 10 d}{8 a}$

Step 3.2

Subtract

$10 d$ from

$7 d$ .

$\frac{- 16 a - 3 d}{8 a}$

Step 3.3

Factor

$- 1$ out of

$- 16 a$ .

$\frac{- (16 a) - 3 d}{8 a}$

Step 3.4

Factor

$- 1$ out of

$- 3 d$ .

$\frac{- (16 a) - (3 d)}{8 a}$

Step 3.5

Factor

$- 1$ out of

$- (16 a) - (3 d)$ .

$\frac{- (16 a + 3 d)}{8 a}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite

$- (16 a + 3 d)$ as

$- 1 (16 a + 3 d)$ .

$\frac{- 1 (16 a + 3 d)}{8 a}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{16 a + 3 d}{8 a}$

$- \frac{16 a + 3 d}{8 a}$

$- \frac{16 a + 3 d}{8 a}$

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