Solve 3/x+1-2/frac{1{4}-2/x^2-1}

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

Evaluate

$$\frac{4\left(1-2x\right)\left(x-1\right)}{x^{2}-9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+1}{x+1}.

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

Since \frac{3}{x+1} and \frac{2\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3-2\left(x+1\right).

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

Combine like terms in 3-2x-2.

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

Factor x^{2}-1.

$$\frac{\frac{1-2x}{x+1}}{\frac{1}{4}-\frac{2}{\left(x-1\right)\left(x+1\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and \left(x-1\right)\left(x+1\right) is 4\left(x-1\right)\left(x+1\right). Multiply \frac{1}{4} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}. Multiply \frac{2}{\left(x-1\right)\left(x+1\right)} times \frac{4}{4}.

$$\frac{\frac{1-2x}{x+1}}{\frac{\left(x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}-\frac{2\times 4}{4\left(x-1\right)\left(x+1\right)}}$$

Since \frac{\left(x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)} and \frac{2\times 4}{4\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2x}{x+1}}{\frac{\left(x-1\right)\left(x+1\right)-2\times 4}{4\left(x-1\right)\left(x+1\right)}}$$

Do the multiplications in \left(x-1\right)\left(x+1\right)-2\times 4.

$$\frac{\frac{1-2x}{x+1}}{\frac{x^{2}+x-x-1-8}{4\left(x-1\right)\left(x+1\right)}}$$

Combine like terms in x^{2}+x-x-1-8.

$$\frac{\frac{1-2x}{x+1}}{\frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)}}$$

Divide \frac{1-2x}{x+1} by \frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)} by multiplying \frac{1-2x}{x+1} by the reciprocal of \frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)}.

$$\frac{\left(1-2x\right)\times 4\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-9\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{4\left(x-1\right)\left(-2x+1\right)}{x^{2}-9}$$

Use the distributive property to multiply 4 by x-1.

$$\frac{\left(4x-4\right)\left(-2x+1\right)}{x^{2}-9}$$

Use the distributive property to multiply 4x-4 by -2x+1 and combine like terms.

$$\frac{-8x^{2}+12x-4}{x^{2}-9}$$

Expand

$$-\frac{4\left(2x^{2}-3x+1\right)}{x^{2}-9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+1}{x+1}.

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

Since \frac{3}{x+1} and \frac{2\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3-2\left(x+1\right).

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

Combine like terms in 3-2x-2.

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

Factor x^{2}-1.

$$\frac{\frac{1-2x}{x+1}}{\frac{1}{4}-\frac{2}{\left(x-1\right)\left(x+1\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and \left(x-1\right)\left(x+1\right) is 4\left(x-1\right)\left(x+1\right). Multiply \frac{1}{4} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}. Multiply \frac{2}{\left(x-1\right)\left(x+1\right)} times \frac{4}{4}.

$$\frac{\frac{1-2x}{x+1}}{\frac{\left(x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}-\frac{2\times 4}{4\left(x-1\right)\left(x+1\right)}}$$

Since \frac{\left(x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)} and \frac{2\times 4}{4\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2x}{x+1}}{\frac{\left(x-1\right)\left(x+1\right)-2\times 4}{4\left(x-1\right)\left(x+1\right)}}$$

Do the multiplications in \left(x-1\right)\left(x+1\right)-2\times 4.

$$\frac{\frac{1-2x}{x+1}}{\frac{x^{2}+x-x-1-8}{4\left(x-1\right)\left(x+1\right)}}$$

Combine like terms in x^{2}+x-x-1-8.

$$\frac{\frac{1-2x}{x+1}}{\frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)}}$$

Divide \frac{1-2x}{x+1} by \frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)} by multiplying \frac{1-2x}{x+1} by the reciprocal of \frac{x^{2}-9}{4\left(x-1\right)\left(x+1\right)}.

$$\frac{\left(1-2x\right)\times 4\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-9\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{4\left(x-1\right)\left(-2x+1\right)}{x^{2}-9}$$

Use the distributive property to multiply 4 by x-1.

$$\frac{\left(4x-4\right)\left(-2x+1\right)}{x^{2}-9}$$

Use the distributive property to multiply 4x-4 by -2x+1 and combine like terms.

$$\frac{-8x^{2}+12x-4}{x^{2}-9}$$