# How do you simplify  (2)/(x) + (2)/(x-1) - (2)/(x-2)?

Mar 12, 2017

$\frac{2 \left({x}^{2} - 4 x + 2\right)}{x \left(x - 1\right) \left(x - 2\right)}$

#### Explanation:

Before adding/subtracting algebraic fractions we require them to have a $\textcolor{b l u e}{\text{common denominator}}$

Multiply numerator/denominator of $\frac{2}{x} \text{ by } \left(x - 1\right) \left(x - 2\right)$

Multiply numerator/denominator of $\frac{2}{x - 1} \text{ by } x \left(x - 2\right)$

Multiply numerator/denominator of $\frac{2}{x - 2} \text{ by } x \left(x - 1\right)$

• 2/xto(2(x-1)(x-2))/(x(x-1)(x-2))=(2x^2-6x+4)/(x(x-1)(x-2))

• 2/(x-1)to(2x(x-2))/(x(x-1)(x-2))=(2x^2-4x)/(x(x-1)(x-2)

• 2/(x-2)to(2x(x-1))/(x(x-1)(x-2))=(2x^2-2x)/(x(x-1)(x-2))

Now the fractions have a common denominator we can add/subtract the numerators leaving the denominator as it is.

Putting the 3 simplifications together.

rArr(2x^2-6x+4+2x^2-4x-(2x^2-2x))/(x(x-1)(x-2)

$= \frac{2 {x}^{2} - 8 x + 4}{x \left(x - 1\right) \left(x - 2\right)}$

$= \frac{2 \left({x}^{2} - 4 x + 2\right)}{x \left(x - 1\right) \left(x - 2\right)}$