Solve frac{2a^{3}+2ab^{2}}{2ax^2-2ax}*x^3-x/a^2x+b^2x*x/x+1

$$\frac { 2 a ^ { 3 } + 2 a b ^ { 2 } } { 2 a x ^ { 2 } - 2 a x } \cdot \frac { x ^ { 3 } - x } { a ^ { 2 } x + b ^ { 2 } x } \cdot \frac { x } { x + 1 }$$

Evaluate

$$1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2a^{3}+2ab^{2}}{2ax^{2}-2ax}.

$$\frac{2a\left(a^{2}+b^{2}\right)}{2ax\left(x-1\right)}\times \frac{x^{3}-x}{a^{2}x+b^{2}x}\times \frac{x}{x+1}$$

Cancel out 2a in both numerator and denominator.

$$\frac{a^{2}+b^{2}}{x\left(x-1\right)}\times \frac{x^{3}-x}{a^{2}x+b^{2}x}\times \frac{x}{x+1}$$

Factor the expressions that are not already factored in \frac{x^{3}-x}{a^{2}x+b^{2}x}.

$$\frac{a^{2}+b^{2}}{x\left(x-1\right)}\times \frac{x\left(x-1\right)\left(x+1\right)}{x\left(a^{2}+b^{2}\right)}\times \frac{x}{x+1}$$

Cancel out x in both numerator and denominator.

$$\frac{a^{2}+b^{2}}{x\left(x-1\right)}\times \frac{\left(x-1\right)\left(x+1\right)}{a^{2}+b^{2}}\times \frac{x}{x+1}$$

Multiply \frac{a^{2}+b^{2}}{x\left(x-1\right)} times \frac{\left(x-1\right)\left(x+1\right)}{a^{2}+b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+b^{2}\right)\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)\left(a^{2}+b^{2}\right)}\times \frac{x}{x+1}$$

Cancel out \left(x-1\right)\left(a^{2}+b^{2}\right) in both numerator and denominator.

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

Multiply \frac{x+1}{x} times \frac{x}{x+1} by multiplying numerator times numerator and denominator times denominator.

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

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

$$1$$

Factor

$$1$$