Solve x^2/x^2-1*x^2-5x+4/x^2-4x

$$\frac { x ^ { 2 } } { x ^ { 2 } - 1 } \cdot \frac { x ^ { 2 } - 5 x + 4 } { x ^ { 2 } - 4 x }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x+4}{x^{2}-4x}.

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

Cancel out x-4 in both numerator and denominator.

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

Multiply \frac{x^{2}}{x^{2}-1} times \frac{x-1}{x} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x+4}{x^{2}-4x}.

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

Cancel out x-4 in both numerator and denominator.

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

Multiply \frac{x^{2}}{x^{2}-1} times \frac{x-1}{x} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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