Solve 4/x-1-4x^2/(x-1)^2divx/x-1

$$\frac { 4 } { x - 1 } - \frac { 4 x ^ { 2 } } { ( x - 1 ) ^ { 2 } } \div \frac { x } { x - 1 }$$

Evaluate

$$-4$$

Short Solution Steps

Divide \frac{4x^{2}}{\left(x-1\right)^{2}} by \frac{x}{x-1} by multiplying \frac{4x^{2}}{\left(x-1\right)^{2}} by the reciprocal of \frac{x}{x-1}.

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

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

$$\frac{4}{x-1}-\frac{4x}{x-1}$$

Since \frac{4}{x-1} and \frac{4x}{x-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-4x}{x-1}$$

Factor the expressions that are not already factored in \frac{4-4x}{x-1}.

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

Extract the negative sign in 1-x.

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

Cancel out x-1 in both numerator and denominator.

$$-4$$

Factor

$$-4$$