Solve frac{x^{2}-1}{x^3-50+2x^2-25x}:x+1/2x^3-20x^2+50x

$$\frac { x ^ { 2 } - 1 } { x ^ { 3 } - 50 + 2 x ^ { 2 } - 25 x } : \frac { x + 1 } { 2 x ^ { 3 } - 20 x ^ { 2 } + 50 x }$$

Evaluate

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

Short Solution Steps

Divide \frac{x^{2}-1}{x^{3}-50+2x^{2}-25x} by \frac{x+1}{2x^{3}-20x^{2}+50x} by multiplying \frac{x^{2}-1}{x^{3}-50+2x^{2}-25x} by the reciprocal of \frac{x+1}{2x^{3}-20x^{2}+50x}.

$$\frac{\left(x^{2}-1\right)\left(2x^{3}-20x^{2}+50x\right)}{\left(x^{3}-50+2x^{2}-25x\right)\left(x+1\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{2x^{3}-12x^{2}+10x}{x^{2}+7x+10}$$

Expand

$$\frac{2\left(x^{3}-6x^{2}+5x\right)}{x^{2}+7x+10}$$

Short Solution Steps

Divide \frac{x^{2}-1}{x^{3}-50+2x^{2}-25x} by \frac{x+1}{2x^{3}-20x^{2}+50x} by multiplying \frac{x^{2}-1}{x^{3}-50+2x^{2}-25x} by the reciprocal of \frac{x+1}{2x^{3}-20x^{2}+50x}.

$$\frac{\left(x^{2}-1\right)\left(2x^{3}-20x^{2}+50x\right)}{\left(x^{3}-50+2x^{2}-25x\right)\left(x+1\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{2x^{3}-12x^{2}+10x}{x^{2}+7x+10}$$