Solve by Factoring x/30-1/(5x)=1/6

$\frac{x}{30} - \frac{1}{5 x} = \frac{1}{6}$

Step 1

Subtract $\frac{1}{6}$ from both sides of the equation.

$\frac{x}{30} - \frac{1}{5 x} - \frac{1}{6} = 0$

Step 2

To write $\frac{x}{30}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x}{30} \cdot \frac{x}{x} - \frac{1}{5 x} - \frac{1}{6} = 0$

Step 3

To write $- \frac{1}{5 x}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{30} \cdot \frac{x}{x} - \frac{1}{5 x} \cdot \frac{6}{6} - \frac{1}{6} = 0$

Step 4

Write each expression with a common denominator of $30 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{30}$ by $\frac{x}{x}$ .

$\frac{x \cdot x}{30 x} - \frac{1}{5 x} \cdot \frac{6}{6} - \frac{1}{6} = 0$

Multiply $\frac{1}{5 x}$ by $\frac{6}{6}$ .

$\frac{x \cdot x}{30 x} - \frac{6}{5 x \cdot 6} - \frac{1}{6} = 0$

Multiply $6$ by $5$ .

$\frac{x \cdot x}{30 x} - \frac{6}{30 x} - \frac{1}{6} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot x - 6}{30 x} - \frac{1}{6} = 0$

Step 6

Multiply $x$ by $x$ .

$\frac{x^{2} - 6}{30 x} - \frac{1}{6} = 0$

Step 7

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{x^{2} - 6}{30 x} - \frac{1}{6} \cdot \frac{5 x}{5 x} = 0$

Step 8

Write each expression with a common denominator of $30 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{5 x}{5 x}$ .

$\frac{x^{2} - 6}{30 x} - \frac{5 x}{6 (5 x)} = 0$

Multiply $5$ by $6$ .

$\frac{x^{2} - 6}{30 x} - \frac{5 x}{30 x} = 0$

Step 9

Combine the numerators over the common denominator.

$\frac{x^{2} - 6 - 5 x}{30 x} = 0$

Step 10

Factor $x^{2} - 6 - 5 x$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 5$ .

$- 6, 1$

Write the factored form using these integers.

$\frac{(x - 6) (x + 1)}{30 x} = 0$

Step 11

Set the numerator equal to zero.

$(x - 6) (x + 1) = 0$

Step 12

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 6 = 0$

$x + 1 = 0$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 6) (x + 1) = 0$ true.

$x = 6, - 1$

Solve by Factoring x/30-1/(5x)=1/6

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