Basic Math Examples

$\frac{a}{5 - a} + \frac{2 a - 5}{a - 5}$

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $a$ .

$\frac{a}{5 - a} + \frac{2 a - 5}{- 1 (- a) - 5}$

Step 1.2

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

$\frac{a}{5 - a} + \frac{2 a - 5}{- 1 (- a) - 1 (5)}$

Step 1.3

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

$\frac{a}{5 - a} + \frac{2 a - 5}{- 1 (- a + 5)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{2 a - 5}{- 1 (- a + 5)}$ to the numerator.

$\frac{a}{5 - a} + \frac{- (2 a - 5)}{- a + 5}$

Step 1.4.2

Reorder terms.

$\frac{a}{- a + 5} + \frac{- (2 a - 5)}{- a + 5}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{a - (2 a - 5)}{- a + 5}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{a - (2 a) - - 5}{- a + 5}$

Step 2.2

Multiply $2$ by $- 1$ .

$\frac{a - 2 a - - 5}{- a + 5}$

Step 2.3

Multiply $- 1$ by $- 5$ .

$\frac{a - 2 a + 5}{- a + 5}$

Step 2.4

Subtract $2 a$ from $a$ .

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

Step 3

Cancel the common factor of $- a + 5$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$1$