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

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

To write $\frac{2 x - 3}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{2 x - 3}{x - 1} \cdot \frac{x + 1}{x + 1} - \frac{2 x + 1}{x + 1}$

To write $- \frac{2 x + 1}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{2 x - 3}{x - 1} \cdot \frac{x + 1}{x + 1} - \frac{2 x + 1}{x + 1} \cdot \frac{x - 1}{x - 1}$

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

Multiply $\frac{2 x - 3}{x - 1}$ by $\frac{x + 1}{x + 1}$ .

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

Multiply $\frac{2 x + 1}{x + 1}$ by $\frac{x - 1}{x - 1}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Expand $(2 x - 3) (x + 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $1$ .

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

Multiply $- 3$ by $1$ .

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

Subtract $3 x$ from $2 x$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $1$ .

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

Expand $(- 2 x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 2$ .

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

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

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

Multiply $- 1$ by $- 1$ .

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

Subtract $x$ from $2 x$ .

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

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

$\frac{- x - 3 + 0 + x + 1}{(x + 1) (x - 1)}$

Add $- x$ and $0$ .

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

Add $- x$ and $x$ .

$\frac{0 - 3 + 1}{(x + 1) (x - 1)}$

Subtract $3$ from $0$ .

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

Add $- 3$ and $1$ .

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

Move the negative in front of the fraction.

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

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

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