Solve x^2+x-6/x^2+4x-5*x^2-25/x^2+2x-25=

$$\frac { x ^ { 2 } + x - 6 } { x ^ { 2 } + 4 x - 5 } \cdot \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 2 x - 25 } =$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}+x-6}{x^{2}+4x-5} times \frac{x^{2}-25}{x^{2}+2x-25} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+3\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)\left(x-\left(\sqrt{26}-1\right)\right)\left(x-\left(-\sqrt{26}-1\right)\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+3\right)}{\left(x-1\right)\left(x-\left(\sqrt{26}-1\right)\right)\left(x-\left(-\sqrt{26}-1\right)\right)}$$

Expand the expression.

$$\frac{x^{3}-4x^{2}-11x+30}{x^{3}+x^{2}-27x+25}$$

Expand

$$\frac{x^{3}-4x^{2}-11x+30}{\left(x-1\right)\left(x^{2}+2x-25\right)}$$

Short Solution Steps

Multiply \frac{x^{2}+x-6}{x^{2}+4x-5} times \frac{x^{2}-25}{x^{2}+2x-25} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+3\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)\left(x-\left(\sqrt{26}-1\right)\right)\left(x-\left(-\sqrt{26}-1\right)\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{\left(x-5\right)\left(x-2\right)\left(x+3\right)}{\left(x-1\right)\left(x-\left(\sqrt{26}-1\right)\right)\left(x-\left(-\sqrt{26}-1\right)\right)}$$

Expand the expression.

$$\frac{x^{3}-4x^{2}-11x+30}{x^{3}+x^{2}-27x+25}$$