Basic Math Examples

$\frac{5 a - 3 t}{6 a} - \frac{10 a - 9 t}{6 a}$

Step 1

Combine the numerators over the common denominator.

$\frac{5 a - 3 t - (10 a - 9 t)}{6 a}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{5 a - 3 t - (10 a) - (- 9 t)}{6 a}$

Step 2.2

Multiply $10$ by $- 1$ .

$\frac{5 a - 3 t - 10 a - (- 9 t)}{6 a}$

Step 2.3

Multiply $- 9$ by $- 1$ .

$\frac{5 a - 3 t - 10 a + 9 t}{6 a}$

$\frac{5 a - 3 t - 10 a + 9 t}{6 a}$

Step 3

Simplify terms.

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Step 3.1

Subtract $10 a$ from $5 a$ .

$\frac{- 5 a - 3 t + 9 t}{6 a}$

Step 3.2

Add $- 3 t$ and $9 t$ .

$\frac{- 5 a + 6 t}{6 a}$

Step 3.3

Factor $- 1$ out of $- 5 a$ .

$\frac{- (5 a) + 6 t}{6 a}$

Step 3.4

Factor $- 1$ out of $6 t$ .

$\frac{- (5 a) - (- 6 t)}{6 a}$

Step 3.5

Factor $- 1$ out of $- (5 a) - (- 6 t)$ .

$\frac{- (5 a - 6 t)}{6 a}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite $- (5 a - 6 t)$ as $- 1 (5 a - 6 t)$ .

$\frac{- 1 (5 a - 6 t)}{6 a}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{5 a - 6 t}{6 a}$

$- \frac{5 a - 6 t}{6 a}$

$- \frac{5 a - 6 t}{6 a}$

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