Basic Math Examples

$\frac{5}{a + 3} + \frac{- 6 a - 3}{a^{2} + 3 a} - \frac{4 - a}{a}$

Step 1

Simplify each term.

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Step 1.1

Factor $3$ out of $- 6 a - 3$ .

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Step 1.1.1

Factor $3$ out of $- 6 a$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a) - 3}{a^{2} + 3 a} - \frac{4 - a}{a}$

Step 1.1.2

Factor $3$ out of $- 3$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a) + 3 (- 1)}{a^{2} + 3 a} - \frac{4 - a}{a}$

Step 1.1.3

Factor $3$ out of $3 (- 2 a) + 3 (- 1)$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a - 1)}{a^{2} + 3 a} - \frac{4 - a}{a}$

Step 1.2

Factor $a$ out of $a^{2} + 3 a$ .

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Step 1.2.1

Factor $a$ out of $a^{2}$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a - 1)}{a \cdot a + 3 a} - \frac{4 - a}{a}$

Step 1.2.2

Factor $a$ out of $3 a$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a - 1)}{a \cdot a + a \cdot 3} - \frac{4 - a}{a}$

Step 1.2.3

Factor $a$ out of $a \cdot a + a \cdot 3$ .

$\frac{5}{a + 3} + \frac{3 (- 2 a - 1)}{a (a + 3)} - \frac{4 - a}{a}$

Step 2

To write $\frac{5}{a + 3}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{5}{a + 3} \cdot \frac{a}{a} + \frac{3 (- 2 a - 1)}{a (a + 3)} - \frac{4 - a}{a}$

Step 3

Write each expression with a common denominator of $(a + 3) a$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{a + 3}$ by $\frac{a}{a}$ .

$\frac{5 a}{(a + 3) a} + \frac{3 (- 2 a - 1)}{a (a + 3)} - \frac{4 - a}{a}$

Step 3.2

Reorder the factors of $(a + 3) a$ .

$\frac{5 a}{a (a + 3)} + \frac{3 (- 2 a - 1)}{a (a + 3)} - \frac{4 - a}{a}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 a + 3 (- 2 a - 1)}{a (a + 3)} - \frac{4 - a}{a}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Apply the distributive property.

$\frac{5 a + 3 (- 2 a) + 3 \cdot - 1}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.1.2

Multiply $- 2$ by $3$ .

$\frac{5 a - 6 a + 3 \cdot - 1}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.1.3

Multiply $3$ by $- 1$ .

$\frac{5 a - 6 a - 3}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.1.4

Subtract $6 a$ from $5 a$ .

$\frac{- a - 3}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2

Cancel the common factor of $- a - 3$ and $a + 3$ .

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Step 5.2.1

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

$\frac{- (a) - 3}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (a) - 1 (3)}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2.3

Factor $- 1$ out of $- (a) - 1 (3)$ .

$\frac{- (a + 3)}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2.4

Rewrite $- (a + 3)$ as $- 1 (a + 3)$ .

$\frac{- 1 (a + 3)}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2.5

Cancel the common factor.

$\frac{- 1 (a + 3)}{a (a + 3)} - \frac{4 - a}{a}$

Step 5.2.6

Rewrite the expression.

$\frac{- 1}{a} - \frac{4 - a}{a}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{1}{a} - \frac{4 - a}{a}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 1 - (4 - a)}{a}$

Step 7

Simplify each term.

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Step 7.1

Apply the distributive property.

$\frac{- 1 - 1 \cdot 4 - - a}{a}$

Step 7.2

Multiply $- 1$ by $4$ .

$\frac{- 1 - 4 - - a}{a}$

Step 7.3

Multiply $- - a$ .

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Step 7.3.1

Multiply $- 1$ by $- 1$ .

$\frac{- 1 - 4 + 1 a}{a}$

Step 7.3.2

Multiply $a$ by $1$ .

$\frac{- 1 - 4 + a}{a}$

Step 8

Simplify with factoring out.

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Step 8.1

Subtract $4$ from $- 1$ .

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

Step 8.2

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

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

Step 8.3

Factor $- 1$ out of $a$ .

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

Step 8.4

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

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

Step 8.5

Move the negative in front of the fraction.

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