Solve (x^2-1/x^2+3x-10)div(x^2-3x-4/x^2-25)=

$$( \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 3 x - 10 } ) \div ( \frac { x ^ { 2 } - 3 x - 4 } { x ^ { 2 } - 25 } ) =$$

Evaluate

$$\frac{\left(x-5\right)\left(x-1\right)}{\left(x-4\right)\left(x-2\right)}$$

Short Solution Steps

Divide \frac{x^{2}-1}{x^{2}+3x-10} by \frac{x^{2}-3x-4}{x^{2}-25} by multiplying \frac{x^{2}-1}{x^{2}+3x-10} by the reciprocal of \frac{x^{2}-3x-4}{x^{2}-25}.

$$\frac{\left(x^{2}-1\right)\left(x^{2}-25\right)}{\left(x^{2}+3x-10\right)\left(x^{2}-3x-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x+1\right)\left(x+5\right) in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-1\right)}{\left(x-4\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{x^{2}-6x+5}{x^{2}-6x+8}$$

Expand

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

Short Solution Steps

Divide \frac{x^{2}-1}{x^{2}+3x-10} by \frac{x^{2}-3x-4}{x^{2}-25} by multiplying \frac{x^{2}-1}{x^{2}+3x-10} by the reciprocal of \frac{x^{2}-3x-4}{x^{2}-25}.

$$\frac{\left(x^{2}-1\right)\left(x^{2}-25\right)}{\left(x^{2}+3x-10\right)\left(x^{2}-3x-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x+1\right)\left(x+5\right) in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-1\right)}{\left(x-4\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{x^{2}-6x+5}{x^{2}-6x+8}$$