Solve f(x)=2/x+1/x(x-1)

$$f ( x ) = \frac { 2 } { x } + \frac { 1 } { x ( x - 1 ) }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(x-1\right)+1.

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

Combine like terms in 2x-2+1.

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

Expand x\left(x-1\right).

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(x-1\right)+1.

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

Combine like terms in 2x-2+1.

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

Expand x\left(x-1\right).

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