Solve 2/a-1+2a-4/a-1+1/2-a

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

Evaluate

$$\frac{5-2a}{2-a}$$

Short Solution Steps

Since \frac{2}{a-1} and \frac{2a-4}{a-1} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2+2a-4.

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

Factor the expressions that are not already factored in \frac{-2+2a}{a-1}.

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

Cancel out a-1 in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in 4-2a+1.

$$\frac{5-2a}{2-a}$$

Expand

$$\frac{5-2a}{2-a}$$

Short Solution Steps

Since \frac{2}{a-1} and \frac{2a-4}{a-1} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2+2a-4.

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

Factor the expressions that are not already factored in \frac{-2+2a}{a-1}.

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

Cancel out a-1 in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in 4-2a+1.

$$\frac{5-2a}{2-a}$$