Solve by Factoring 1/3+1/5=1/x

$\frac{1}{3} + \frac{1}{5} = \frac{1}{x}$

Step 1

Subtract $\frac{1}{x}$ from both sides of the equation.

$\frac{1}{3} + \frac{1}{5} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{3} + \frac{1}{5} - \frac{1}{x}$ .

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5} - \frac{1}{x} = 0$

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{3}{3} - \frac{1}{x} = 0$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{5}{3 \cdot 5} + \frac{1}{5} \cdot \frac{3}{3} - \frac{1}{x} = 0$

Multiply $3$ by $5$ .

$\frac{5}{15} + \frac{1}{5} \cdot \frac{3}{3} - \frac{1}{x} = 0$

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{5}{15} + \frac{3}{5 \cdot 3} - \frac{1}{x} = 0$

Multiply $5$ by $3$ .

$\frac{5}{15} + \frac{3}{15} - \frac{1}{x} = 0$

Combine the numerators over the common denominator.

$\frac{5 + 3}{15} - \frac{1}{x} = 0$

Add $5$ and $3$ .

$\frac{8}{15} - \frac{1}{x} = 0$

Step 3

To write $\frac{8}{15}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{8}{15} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{8}{15} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{15}{15} = 0$

Step 5

Write each expression with a common denominator of $15 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{15}$ by $\frac{x}{x}$ .

$\frac{8 x}{15 x} - \frac{1}{x} \cdot \frac{15}{15} = 0$

Multiply $\frac{1}{x}$ by $\frac{15}{15}$ .

$\frac{8 x}{15 x} - \frac{15}{x \cdot 15} = 0$

Reorder the factors of $x \cdot 15$ .

$\frac{8 x}{15 x} - \frac{15}{15 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{8 x - 15}{15 x} = 0$

Step 7

Set the numerator equal to zero.

$8 x - 15 = 0$

Step 8

Solve the equation for $x$ .

Add $15$ to both sides of the equation.

$8 x = 15$

Divide each term in $8 x = 15$ by $8$ and simplify.

Divide each term in $8 x = 15$ by $8$ .

$\frac{8 x}{8} = \frac{15}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{15}{8}$

Divide $x$ by $1$ .

$x = \frac{15}{8}$

Solve by Factoring 1/3+1/5=1/x

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