Algebra Examples

$\frac{1}{3 x - 2} + \frac{5}{x} = 0$

Step 1

To write $\frac{1}{3 x - 2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{3 x - 2} \cdot \frac{x}{x} + \frac{5}{x} = 0$

Step 2

To write $\frac{5}{x}$ as a fraction with a common denominator, multiply by $\frac{3 x - 2}{3 x - 2}$ .

$\frac{1}{3 x - 2} \cdot \frac{x}{x} + \frac{5}{x} \cdot \frac{3 x - 2}{3 x - 2} = 0$

Step 3

Write each expression with a common denominator of $(3 x - 2) x$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{1}{3 x - 2}$ by $\frac{x}{x}$ .

$\frac{x}{(3 x - 2) x} + \frac{5}{x} \cdot \frac{3 x - 2}{3 x - 2} = 0$

Step 3.2

Multiply $\frac{5}{x}$ by $\frac{3 x - 2}{3 x - 2}$ .

$\frac{x}{(3 x - 2) x} + \frac{5 (3 x - 2)}{x (3 x - 2)} = 0$

Step 3.3

Reorder the factors of $(3 x - 2) x$ .

$\frac{x}{x (3 x - 2)} + \frac{5 (3 x - 2)}{x (3 x - 2)} = 0$

Step 4

Combine the numerators over the common denominator.

$\frac{x + 5 (3 x - 2)}{x (3 x - 2)} = 0$

Step 5

Rewrite $\frac{x + 5 (3 x - 2)}{x (3 x - 2)}$ in a factored form.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{x + 5 (3 x) + 5 \cdot - 2}{x (3 x - 2)} = 0$

Step 5.2

Multiply $3$ by $5$ .

$\frac{x + 15 x + 5 \cdot - 2}{x (3 x - 2)} = 0$

Step 5.3

Multiply $5$ by $- 2$ .

$\frac{x + 15 x - 10}{x (3 x - 2)} = 0$

Step 5.4

Add $x$ and $15 x$ .

$\frac{16 x - 10}{x (3 x - 2)} = 0$

Step 5.5

Factor $2$ out of $16 x - 10$ .

Tap for more steps...

Step 5.5.1

Factor $2$ out of $16 x$ .

$\frac{2 (8 x) - 10}{x (3 x - 2)} = 0$

Step 5.5.2

Factor $2$ out of $- 10$ .

$\frac{2 (8 x) + 2 (- 5)}{x (3 x - 2)} = 0$

Step 5.5.3

Factor $2$ out of $2 (8 x) + 2 (- 5)$ .

$\frac{2 (8 x - 5)}{x (3 x - 2)} = 0$

Step 6

Set the numerator equal to zero.

$2 (8 x - 5) = 0$

Step 7

Solve the equation for $x$ .

Tap for more steps...

Step 7.1

Divide each term in $2 (8 x - 5) = 0$ by $2$ and simplify.

Tap for more steps...

Step 7.1.1

Divide each term in $2 (8 x - 5) = 0$ by $2$ .

$\frac{2 (8 x - 5)}{2} = \frac{0}{2}$

Step 7.1.2

Simplify the left side.

Tap for more steps...

Step 7.1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.2.1.1

Cancel the common factor.

$\frac{2 (8 x - 5)}{2} = \frac{0}{2}$

Step 7.1.2.1.2

Divide $8 x - 5$ by $1$ .

$8 x - 5 = \frac{0}{2}$

Step 7.1.3

Simplify the right side.

Tap for more steps...

Step 7.1.3.1

Divide $0$ by $2$ .

$8 x - 5 = 0$

Step 7.2

Add $5$ to both sides of the equation.

$8 x = 5$

Step 7.3

Divide each term in $8 x = 5$ by $8$ and simplify.

Tap for more steps...

Step 7.3.1

Divide each term in $8 x = 5$ by $8$ .

$\frac{8 x}{8} = \frac{5}{8}$

Step 7.3.2

Simplify the left side.

Tap for more steps...

Step 7.3.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 7.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{5}{8}$

Step 7.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{8}$