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

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

Evaluate

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

Short Solution Steps

Use the distributive property to multiply 2 by x-1.

$$2x-2+a\times \frac{1}{x-1}$$

Express a\times \frac{1}{x-1} as a single fraction.

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

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

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

Use the distributive property to multiply 2 by x-1.

$$2x-2+a\times \frac{1}{x-1}$$

Express a\times \frac{1}{x-1} as a single fraction.

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

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

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

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

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

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

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

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

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