Solve by Factoring 2/x+1/2=5/x

$\frac{2}{x} + \frac{1}{2} = \frac{5}{x}$

Step 1

Subtract $\frac{5}{x}$ from both sides of the equation.

$\frac{2}{x} + \frac{1}{2} - \frac{5}{x} = 0$

Step 2

Simplify $\frac{2}{x} + \frac{1}{2} - \frac{5}{x}$ .

Combine the numerators over the common denominator.

$\frac{2 - 5}{x} + \frac{1}{2} = 0$

Subtract $5$ from $2$ .

$\frac{- 3}{x} + \frac{1}{2} = 0$

Move the negative in front of the fraction.

$- \frac{3}{x} + \frac{1}{2} = 0$

Step 3

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{x} \cdot \frac{2}{2} + \frac{1}{2} = 0$

Step 4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- \frac{3}{x} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{x}{x} = 0$

Step 5

Write each expression with a common denominator of $x \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x}$ by $\frac{2}{2}$ .

$- \frac{3 \cdot 2}{x \cdot 2} + \frac{1}{2} \cdot \frac{x}{x} = 0$

Multiply $\frac{1}{2}$ by $\frac{x}{x}$ .

$- \frac{3 \cdot 2}{x \cdot 2} + \frac{x}{2 x} = 0$

Reorder the factors of $x \cdot 2$ .

$- \frac{3 \cdot 2}{2 x} + \frac{x}{2 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 2 + x}{2 x} = 0$

Step 7

Multiply $- 3$ by $2$ .

$\frac{- 6 + x}{2 x} = 0$

Step 8

Set the numerator equal to zero.

$- 6 + x = 0$

Step 9

Add $6$ to both sides of the equation.

$x = 6$