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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

$$\frac{2a^{2}-4a+2}{a\left(a-2\right)}$$

Expand a\left(a-2\right).

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

$$\frac{2a^{2}-4a+2}{a\left(a-2\right)}$$

Expand a\left(a-2\right).

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