Simplify x/(x+3)-(4(x+3))/(x-1)

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

Step 1

To write $\frac{x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

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

Step 2

To write $- \frac{4 (x + 3)}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

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

Step 3

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

Multiply $\frac{x}{x + 3}$ by $\frac{x - 1}{x - 1}$ .

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

Multiply $\frac{4 (x + 3)}{x - 1}$ by $\frac{x + 3}{x + 3}$ .

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

Reorder the factors of $(x - 1) (x + 3)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

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

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot - 1 - 4 (x + 3) (x + 3)}{(x + 3) (x - 1)}$

Move $- 1$ to the left of $x$ .

$\frac{x^{2} - 1 \cdot x - 4 (x + 3) (x + 3)}{(x + 3) (x - 1)}$

Rewrite $- 1 x$ as $- x$ .

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

Apply the distributive property.

$\frac{x^{2} - x + (- 4 x - 4 \cdot 3) (x + 3)}{(x + 3) (x - 1)}$

Multiply $- 4$ by $3$ .

$\frac{x^{2} - x + (- 4 x - 12) (x + 3)}{(x + 3) (x - 1)}$

Expand $(- 4 x - 12) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$\frac{x^{2} - x - 4 x (x + 3) - 12 (x + 3)}{(x + 3) (x - 1)}$

Apply the distributive property.

$\frac{x^{2} - x - 4 x \cdot x - 4 x \cdot 3 - 12 (x + 3)}{(x + 3) (x - 1)}$

Apply the distributive property.

$\frac{x^{2} - x - 4 x \cdot x - 4 x \cdot 3 - 12 x - 12 \cdot 3}{(x + 3) (x - 1)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{x^{2} - x - 4 (x \cdot x) - 4 x \cdot 3 - 12 x - 12 \cdot 3}{(x + 3) (x - 1)}$

Multiply $x$ by $x$ .

$\frac{x^{2} - x - 4 x^{2} - 4 x \cdot 3 - 12 x - 12 \cdot 3}{(x + 3) (x - 1)}$

Multiply $3$ by $- 4$ .

$\frac{x^{2} - x - 4 x^{2} - 12 x - 12 x - 12 \cdot 3}{(x + 3) (x - 1)}$

Multiply $- 12$ by $3$ .

$\frac{x^{2} - x - 4 x^{2} - 12 x - 12 x - 36}{(x + 3) (x - 1)}$

Subtract $12 x$ from $- 12 x$ .

$\frac{x^{2} - x - 4 x^{2} - 24 x - 36}{(x + 3) (x - 1)}$

Subtract $4 x^{2}$ from $x^{2}$ .

$\frac{- 3 x^{2} - x - 24 x - 36}{(x + 3) (x - 1)}$

Subtract $24 x$ from $- x$ .

$\frac{- 3 x^{2} - 25 x - 36}{(x + 3) (x - 1)}$

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- 3 x^{2}$ .

$\frac{- (3 x^{2}) - 25 x - 36}{(x + 3) (x - 1)}$

Factor $- 1$ out of $- 25 x$ .

$\frac{- (3 x^{2}) - (25 x) - 36}{(x + 3) (x - 1)}$

Factor $- 1$ out of $- (3 x^{2}) - (25 x)$ .

$\frac{- (3 x^{2} + 25 x) - 36}{(x + 3) (x - 1)}$

Rewrite $- 36$ as $- 1 (36)$ .

$\frac{- (3 x^{2} + 25 x) - 1 (36)}{(x + 3) (x - 1)}$

Factor $- 1$ out of $- (3 x^{2} + 25 x) - 1 (36)$ .

$\frac{- (3 x^{2} + 25 x + 36)}{(x + 3) (x - 1)}$

Simplify the expression.

Rewrite $- (3 x^{2} + 25 x + 36)$ as $- 1 (3 x^{2} + 25 x + 36)$ .

$\frac{- 1 (3 x^{2} + 25 x + 36)}{(x + 3) (x - 1)}$

Move the negative in front of the fraction.

$- \frac{3 x^{2} + 25 x + 36}{(x + 3) (x - 1)}$

Simplify x/(x+3)-(4(x+3))/(x-1)

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