Basic Math Examples

$\frac{9 v + 5}{v - 5} + \frac{5 v}{5 - v}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{9 v + 5}{v - 5} + \frac{5 v}{- 1 (- 5) - v}$

Step 1.2

Factor $- 1$ out of $- v$ .

$\frac{9 v + 5}{v - 5} + \frac{5 v}{- 1 (- 5) - (v)}$

Step 1.3

Factor $- 1$ out of $- 1 (- 5) - (v)$ .

$\frac{9 v + 5}{v - 5} + \frac{5 v}{- 1 (- 5 + v)}$

Step 1.4

Simplify the expression.

Tap for more steps...

Step 1.4.1

Move a negative from the denominator of $\frac{5 v}{- 1 (- 5 + v)}$ to the numerator.

$\frac{9 v + 5}{v - 5} + \frac{- (5 v)}{- 5 + v}$

Step 1.4.2

Reorder terms.

$\frac{9 v + 5}{v - 5} + \frac{- (5 v)}{v - 5}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{9 v + 5 - (5 v)}{v - 5}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Multiply $- 1$ by $5$ .

$\frac{9 v + 5 - 5 v}{v - 5}$

Step 2.2

Subtract $5 v$ from $9 v$ .

$\frac{4 v + 5}{v - 5}$