# How do you simplify 3/(x-3) - 1/x?

Mar 11, 2018

$\frac{2 x + 3}{{x}^{2} + 3 x}$

#### Explanation:

First Take The L.C.M of the denominators.

Here L.C.M is $x \left(x - 3\right)$.

Now, you have to make the denominators of the expressions same as L.C.M and to do it, you have to multiply both numerators and denominators of the expresions by specific numbers.

So,

$\frac{3}{x - 3} - \frac{1}{x} = \frac{3 x}{x \left(x - 3\right)} - \frac{x - 3}{x \left(x - 3\right)}$

Now, We can subtract them like we subtract like fractions.

So, $\frac{3}{x - 3} - \frac{1}{x} = \frac{3 x}{x \left(x - 3\right)} - \frac{x - 3}{x \left(x - 3\right)} = \frac{3 x - \left(x - 3\right)}{x \left(x - 3\right)} = \frac{3 x - x + 3}{{x}^{2} + 3 x} = \frac{2 x + 3}{{x}^{2} + 3 x}$

Hence explained.