Algebra Examples

$\frac{x}{4} = \frac{9}{2 x}$

Step 1

Subtract $\frac{9}{2 x}$ from both sides of the equation.

$\frac{x}{4} - \frac{9}{2 x} = 0$

Step 2

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x}{4} \cdot \frac{x}{x} - \frac{9}{2 x} = 0$

Step 3

To write $- \frac{9}{2 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} \cdot \frac{x}{x} - \frac{9}{2 x} \cdot \frac{2}{2} = 0$

Step 4

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{x}{4}$ by $\frac{x}{x}$ .

$\frac{x \cdot x}{4 x} - \frac{9}{2 x} \cdot \frac{2}{2} = 0$

Step 4.2

Multiply $\frac{9}{2 x}$ by $\frac{2}{2}$ .

$\frac{x \cdot x}{4 x} - \frac{9 \cdot 2}{2 x \cdot 2} = 0$

Step 4.3

Multiply $2$ by $2$ .

$\frac{x \cdot x}{4 x} - \frac{9 \cdot 2}{4 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot x - 9 \cdot 2}{4 x} = 0$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $x$ by $x$ .

$\frac{x^{2} - 9 \cdot 2}{4 x} = 0$

Step 6.2

Multiply $- 9$ by $2$ .

$\frac{x^{2} - 18}{4 x} = 0$

Step 7

Set the numerator equal to zero.

$x^{2} - 18 = 0$

Step 8

Solve the equation for $x$ .

Tap for more steps...

Step 8.1

Add $18$ to both sides of the equation.

$x^{2} = 18$

Step 8.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{18}$

Step 8.3

Simplify $\pm \sqrt{18}$ .

Tap for more steps...

Step 8.3.1

Rewrite $18$ as $3^{2} \cdot 2$ .

Tap for more steps...

Step 8.3.1.1

Factor $9$ out of $18$ .

$x = \pm \sqrt{9 (2)}$

Step 8.3.1.2

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2} \cdot 2}$

Step 8.3.2

Pull terms out from under the radical.

$x = \pm 3 \sqrt{2}$

Step 8.4

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 8.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 3 \sqrt{2}$

Step 8.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3 \sqrt{2}$

Step 8.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$x = 4.24264068 \dots, - 4.24264068 \dots$