# How do you solve 1/2 + 2/x = 1/x?

Jul 24, 2017

$- 2$

#### Explanation:

we need to clear all the denominators first.

multiply everything by$x$

$\frac{1}{2} x + 2 \cancel{\frac{x}{x}} = {\cancel{\frac{x}{x}}}^{1}$

$\frac{1}{2} x + 2 = 1$

multiply everything by $2$

$2 \times \frac{1}{2} x + 2 \times 2 = 1 \times 2$

$\implies x + 4 = 2$

subtract $4$

$x + 4 - 4 = 2 - 4$

$\therefore x = - 2$

Jul 24, 2017

$x = - 2$

#### Explanation:

Our goal is to isolate the variable, $x$. Start by moving all of the $x$ terms to the same side.

$\frac{1}{2} = \frac{1}{x} - \frac{2}{x}$

Since both terms on the right share the same denominator, we can combine them.

$\frac{1}{2} = \frac{1 - 2}{x}$

Now we only have one $x$ term. Cross multiply to get rid of the fractions.

$x = 2 \left(1 - 2\right)$

Solve.

$x = - 2$

Jul 24, 2017

$x = - 2$

#### Explanation:

$\frac{1}{2} + \frac{2}{x} = \frac{1}{x} \text{ } \leftarrow$ LCM of denominators $= 2 x$

We have an equation, so we can do anything as long as you do the same to both sides.

Multiply each term by the LCM of the denominators to cancel them.

$\frac{\cancel{2} x \times 1}{\cancel{2}} + \frac{2 \cancel{x} \times 2}{\cancel{x}} = \frac{2 \cancel{x} \times 1}{\cancel{x}}$

This leaves the equation as:

$x + 4 = 2$

$x = 2 - 4$

$x = - 2$