Solve 1+kx-k-2x/(1-x)^2

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{\left(1-x\right)^{2}}{\left(1-x\right)^{2}} and \frac{kx-k-2x}{\left(1-x\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(1-x\right)^{2}+kx-k-2x.

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

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

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

Expand \left(1-x\right)^{2}.

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

Expand

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

Short Solution Steps

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

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

Since \frac{\left(1-x\right)^{2}}{\left(1-x\right)^{2}} and \frac{kx-k-2x}{\left(1-x\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(1-x\right)^{2}+kx-k-2x.

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

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

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

Expand \left(1-x\right)^{2}.

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