Solve (x+5/x(x-1)-6x/x(x-1))div1/x^2

$$( \frac{ x+5 }{ x(x-1) } - \frac{ 6x }{ x(x-1) } ) \div \frac{ 1 }{ { x }^{ 2 } }$$

Evaluate

$$-5x$$

Short Solution Steps

Since \frac{x+5}{x\left(x-1\right)} and \frac{6x}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+5-6x}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Combine like terms in x+5-6x.

$$\frac{\frac{-5x+5}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Factor the expressions that are not already factored in \frac{-5x+5}{x\left(x-1\right)}.

$$\frac{\frac{5\left(-x+1\right)}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Extract the negative sign in 1-x.

$$\frac{\frac{-5\left(x-1\right)}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{\frac{-5}{x}}{\frac{1}{x^{2}}}$$

Divide \frac{-5}{x} by \frac{1}{x^{2}} by multiplying \frac{-5}{x} by the reciprocal of \frac{1}{x^{2}}.

$$\frac{-5x^{2}}{x}$$

Cancel out x in both numerator and denominator.

$$-5x$$

Expand

$$-5x$$

Short Solution Steps

Since \frac{x+5}{x\left(x-1\right)} and \frac{6x}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+5-6x}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Combine like terms in x+5-6x.

$$\frac{\frac{-5x+5}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Factor the expressions that are not already factored in \frac{-5x+5}{x\left(x-1\right)}.

$$\frac{\frac{5\left(-x+1\right)}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Extract the negative sign in 1-x.

$$\frac{\frac{-5\left(x-1\right)}{x\left(x-1\right)}}{\frac{1}{x^{2}}}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{\frac{-5}{x}}{\frac{1}{x^{2}}}$$

Divide \frac{-5}{x} by \frac{1}{x^{2}} by multiplying \frac{-5}{x} by the reciprocal of \frac{1}{x^{2}}.

$$\frac{-5x^{2}}{x}$$

Cancel out x in both numerator and denominator.

$$-5x$$