Simplify (-3x)/4-(x+1)/(x^2-1)

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

Simplify each term.

Move the negative in front of the fraction.

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

Simplify the denominator.

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$- \frac{3 x}{4} - \frac{1}{x - 1}$

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

$- \frac{3 x}{4} \cdot \frac{x - 1}{x - 1} - \frac{1}{x - 1}$

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

$- \frac{3 x}{4} \cdot \frac{x - 1}{x - 1} - \frac{1}{x - 1} \cdot \frac{4}{4}$

Write each expression with a common denominator of $4 (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $\frac{1}{x - 1}$ by $\frac{4}{4}$ .

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

Reorder the factors of $(x - 1) \cdot 4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 3$ .

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

Simplify with factoring out.

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

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

Factor $- 1$ out of $3 x$ .

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

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

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

Rewrite $- 4$ as $- 1 (4)$ .

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

Factor $- 1$ out of $- (3 x^{2} - 3 x) - 1 (4)$ .

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

Simplify the expression.

Rewrite $- (3 x^{2} - 3 x + 4)$ as $- 1 (3 x^{2} - 3 x + 4)$ .

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

Move the negative in front of the fraction.

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

Simplify (-3x)/4-(x+1)/(x^2-1)

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