Simplify 5/(a+3)+(-6a-3)/(a^2+3a)-(4-a)/a

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

Simplify each term.

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

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

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

Factor $3$ out of $- 3$ .

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

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

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

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

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

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

Factor $a$ out of $3 a$ .

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

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

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

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

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

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

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

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

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

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

Simplify terms.

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Combine the numerators over the common denominator.

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

Simplify each term.

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Simplify the numerator.

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Apply the distributive property.

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

Multiply $- 2$ by $3$ .

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

Multiply $3$ by $- 1$ .

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

Subtract $6 a$ from $5 a$ .

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

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

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

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

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

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Factor $- 1$ out of $- 1 - (4 - a)$ .

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Reorder the expression.

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Reorder $4$ and $- a$ .

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

Reorder $- 1$ and $- (- a + 4)$ .

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

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

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

Factor $- 1$ out of $- (- a + 4) - 1 (1)$ .

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

Add $4$ and $1$ .

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

Simplify with factoring out.

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Move the negative in front of the fraction.

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

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

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

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

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

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

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{a - 5}{a}$ by $1$ .

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

Simplify 5/(a+3)+(-6a-3)/(a^2+3a)-(4-a)/a

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