Solve (x(x-1)/(x-1)(x-3)-3/x-3-x/x+1):x-1/x^2-1

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

Evaluate

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Short Solution Steps

Cancel out x-1 in both numerator and denominator.

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

Since \frac{x}{x-3} and \frac{3}{x-3} have the same denominator, subtract them by subtracting their numerators.

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

Cancel out x-3 in both numerator and denominator.

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

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

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

Since \frac{x+1}{x+1} and \frac{x}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x+1-x.

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

Factor the expressions that are not already factored in \frac{x-1}{x^{2}-1}.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{\frac{1}{x+1}}{\frac{1}{x+1}}$$

Divide \frac{1}{x+1} by \frac{1}{x+1} by multiplying \frac{1}{x+1} by the reciprocal of \frac{1}{x+1}.

$$\frac{x+1}{x+1}$$

Cancel out x+1 in both numerator and denominator.

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Factor

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