Solve 1/1-frac{2x{1+x+x^2}}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1+x+x^{2}}{1+x+x^{2}}.

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

Since \frac{1+x+x^{2}}{1+x+x^{2}} and \frac{2x}{1+x+x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 1+x+x^{2}-2x.

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

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

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

Differentiate w.r.t. x

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