Solve x^2-6x+5/x^2-x-20divx-1/x+4divx^2-4x-5/x^2-10x+25

$$\frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } - x - 20 } \div \frac { x - 1 } { x + 4 } \div \frac { x ^ { 2 } - 4 x - 5 } { x ^ { 2 } - 10 x + 25 }$$

Evaluate

$$\frac{x-5}{x+1}$$

Short Solution Steps

Divide \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} by \frac{x^{2}-4x-5}{x^{2}-10x+25} by multiplying \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} by the reciprocal of \frac{x^{2}-4x-5}{x^{2}-10x+25}.

$$\frac{\frac{x^{2}-6x+5}{x^{2}-x-20}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}-6x+5}{x^{2}-x-20}.

$$\frac{\frac{\left(x-5\right)\left(x-1\right)}{\left(x-5\right)\left(x+4\right)}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{\frac{x-1}{x+4}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Express \frac{x-1}{x+4}\left(x^{2}-10x+25\right) as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Express \frac{x-1}{x+4}\left(x^{2}-4x-5\right) as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}}$$

Divide \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} by \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4} by multiplying \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} by the reciprocal of \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}.

$$\frac{\left(x-1\right)\left(x^{2}-10x+25\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)\left(x^{2}-4x-5\right)}$$

Cancel out \left(x-1\right)\left(x+4\right) in both numerator and denominator.

$$\frac{x^{2}-10x+25}{x^{2}-4x-5}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)^{2}}{\left(x-5\right)\left(x+1\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{x-5}{x+1}$$

Expand

$$\frac{x-5}{x+1}$$

Short Solution Steps

Divide \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} by \frac{x^{2}-4x-5}{x^{2}-10x+25} by multiplying \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} by the reciprocal of \frac{x^{2}-4x-5}{x^{2}-10x+25}.

$$\frac{\frac{x^{2}-6x+5}{x^{2}-x-20}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}-6x+5}{x^{2}-x-20}.

$$\frac{\frac{\left(x-5\right)\left(x-1\right)}{\left(x-5\right)\left(x+4\right)}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{\frac{x-1}{x+4}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Express \frac{x-1}{x+4}\left(x^{2}-10x+25\right) as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Express \frac{x-1}{x+4}\left(x^{2}-4x-5\right) as a single fraction.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}}$$

Divide \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} by \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4} by multiplying \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} by the reciprocal of \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}.

$$\frac{\left(x-1\right)\left(x^{2}-10x+25\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)\left(x^{2}-4x-5\right)}$$

Cancel out \left(x-1\right)\left(x+4\right) in both numerator and denominator.

$$\frac{x^{2}-10x+25}{x^{2}-4x-5}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)^{2}}{\left(x-5\right)\left(x+1\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{x-5}{x+1}$$