Solve 4x/x^2-1/2x^2+8/x-1

$$\frac{ \frac{ \frac{ 4x }{ { x }^{ 2 } -1 } }{ 2 { x }^{ 2 } +8 } }{ x-1 }$$

Evaluate

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

Short Solution Steps

Express \frac{\frac{\frac{4x}{x^{2}-1}}{2x^{2}+8}}{x-1} as a single fraction.

$$\frac{\frac{4x}{x^{2}-1}}{\left(2x^{2}+8\right)\left(x-1\right)}$$

Express \frac{\frac{4x}{x^{2}-1}}{\left(2x^{2}+8\right)\left(x-1\right)} as a single fraction.

$$\frac{4x}{\left(x^{2}-1\right)\left(2x^{2}+8\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{2x}{x^{5}-x^{4}+3x^{3}-3x^{2}-4x+4}$$

Differentiate w.r.t. x

$$-\frac{2\left(4x^{4}+x^{3}+7x^{2}+4x+4\right)}{\left(x-1\right)^{3}\left(\left(x+1\right)\left(x^{2}+4\right)\right)^{2}}$$