Solve by Factoring 1/b=6/(5b)+1

$\frac{1}{b} = \frac{6}{5 b} + 1$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{6}{5 b}$ from both sides of the equation.

$\frac{1}{b} - \frac{6}{5 b} = 1$

Subtract $1$ from both sides of the equation.

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

Step 2

Simplify $\frac{1}{b} - \frac{6}{5 b} - 1$ .

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

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

Write each expression with a common denominator of $b \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{b}$ by $\frac{5}{5}$ .

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

Move $5$ to the left of $b$ .

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

Combine the numerators over the common denominator.

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

Subtract $6$ from $5$ .

$\frac{- 1}{5 b} - 1 = 0$

Move the negative in front of the fraction.

$- \frac{1}{5 b} - 1 = 0$

Step 3

Factor $- 1$ out of $- \frac{1}{5 b} - 1$ .

Factor $- 1$ out of $- \frac{1}{5 b}$ .

$- (\frac{1}{5 b}) - 1 = 0$

Rewrite $- 1$ as $- 1 (1)$ .

$- (\frac{1}{5 b}) - 1 \cdot 1 = 0$

Factor $- 1$ out of $- (\frac{1}{5 b}) - 1 (1)$ .

$- (\frac{1}{5 b} + 1) = 0$

Step 4

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

$- (\frac{1}{5 b} + \frac{5 b}{5 b}) = 0$

Step 5

Combine the numerators over the common denominator.

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

Step 6

Set the numerator equal to zero.

$1 + 5 b = 0$

Step 7

Solve the equation for $b$ .

Subtract $1$ from both sides of the equation.

$5 b = - 1$

Divide each term in $5 b = - 1$ by $5$ and simplify.

Divide each term in $5 b = - 1$ by $5$ .

$\frac{5 b}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 b}{5} = \frac{- 1}{5}$

Divide $b$ by $1$ .

$b = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{1}{5}$

Solve by Factoring 1/b=6/(5b)+1

Related Questions

Support LCMGCF.com by disabling your adblocker.