Solve by Factoring 1/(6b^2)+1/(6b)=1/(b^2)

$\frac{1}{6 b^{2}} + \frac{1}{6 b} = \frac{1}{b^{2}}$

Step 1

Subtract $\frac{1}{b^{2}}$ from both sides of the equation.

$\frac{1}{6 b^{2}} + \frac{1}{6 b} - \frac{1}{b^{2}} = 0$

Step 2

Simplify $\frac{1}{6 b^{2}} + \frac{1}{6 b} - \frac{1}{b^{2}}$ .

To write $- \frac{1}{b^{2}}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{6 b} + \frac{1}{6 b^{2}} - \frac{1}{b^{2}} \cdot \frac{6}{6} = 0$

Write each expression with a common denominator of $6 b^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{b^{2}}$ by $\frac{6}{6}$ .

$\frac{1}{6 b} + \frac{1}{6 b^{2}} - \frac{6}{b^{2} \cdot 6} = 0$

Reorder the factors of $b^{2} \cdot 6$ .

$\frac{1}{6 b} + \frac{1}{6 b^{2}} - \frac{6}{6 b^{2}} = 0$

Combine the numerators over the common denominator.

$\frac{1}{6 b} + \frac{1 - 6}{6 b^{2}} = 0$

Subtract $6$ from $1$ .

$\frac{1}{6 b} + \frac{- 5}{6 b^{2}} = 0$

Move the negative in front of the fraction.

$\frac{1}{6 b} - \frac{5}{6 b^{2}} = 0$

Step 3

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

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

Step 4

Write each expression with a common denominator of $6 b^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6 b}$ by $\frac{b}{b}$ .

$\frac{b}{6 b \cdot b} - \frac{5}{6 b^{2}} = 0$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{b}{6 (b \cdot b)} - \frac{5}{6 b^{2}} = 0$

Multiply $b$ by $b$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Set the numerator equal to zero.

$b - 5 = 0$

Step 7

Add $5$ to both sides of the equation.

$b = 5$