Algebra Examples

$\frac{3}{x} + \frac{5}{x} = - 4$

Step 1

Add $4$ to both sides of the equation.

$\frac{3}{x} + \frac{5}{x} + 4 = 0$

Step 2

Simplify $\frac{3}{x} + \frac{5}{x} + 4$ .

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$4 + \frac{3 + 5}{x} = 0$

Step 2.2

Add $3$ and $5$ .

$4 + \frac{8}{x} = 0$

Step 3

Factor $4$ out of $4 + \frac{8}{x}$ .

Tap for more steps...

Step 3.1

Factor $4$ out of $4$ .

$4 (1) + \frac{8}{x} = 0$

Step 3.2

Factor $4$ out of $\frac{8}{x}$ .

$4 \cdot 1 + 4 (\frac{2}{x}) = 0$

Step 3.3

Factor $4$ out of $4 \cdot 1 + 4 \frac{2}{x}$ .

$4 (1 + \frac{2}{x}) = 0$

Step 4

Write $1$ as a fraction with a common denominator.

$4 (\frac{x}{x} + \frac{2}{x}) = 0$

Step 5

Combine the numerators over the common denominator.

$4 (\frac{x + 2}{x}) = 0$

Step 6

Combine $4$ and $\frac{x + 2}{x}$ .

$\frac{4 (x + 2)}{x} = 0$

Step 7

Set the numerator equal to zero.

$4 (x + 2) = 0$

Step 8

Solve the equation for $x$ .

Tap for more steps...

Step 8.1

Divide each term in $4 (x + 2) = 0$ by $4$ and simplify.

Tap for more steps...

Step 8.1.1

Divide each term in $4 (x + 2) = 0$ by $4$ .

$\frac{4 (x + 2)}{4} = \frac{0}{4}$

Step 8.1.2

Simplify the left side.

Tap for more steps...

Step 8.1.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 8.1.2.1.1

Cancel the common factor.

$\frac{4 (x + 2)}{4} = \frac{0}{4}$

Step 8.1.2.1.2

Divide $x + 2$ by $1$ .

$x + 2 = \frac{0}{4}$

Step 8.1.3

Simplify the right side.

Tap for more steps...

Step 8.1.3.1

Divide $0$ by $4$ .

$x + 2 = 0$

Step 8.2

Subtract $2$ from both sides of the equation.

$x = - 2$