Solve the Rational Equation for b 1/(6b^2)+1/(6b)=1/(b^2)

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Since ${\displaystyle 6b^2,6b,b^2}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 6,6,1}$ then find LCM for the variable part ${\displaystyle b^2,b^1,b^2}$.

The LCM is the smallest positive number that all of the numbers divide into evenly.

${\displaystyle 6}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 3}$.

The number ${\displaystyle 1}$ is not a prime number because it only has one positive factor, which is itself.

The LCM of ${\displaystyle 6,6,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

Multiply ${\displaystyle 2}$ by ${\displaystyle 3}$.

The factors for ${\displaystyle b^2}$ are ${\displaystyle b\cdot b}$, which is ${\displaystyle b}$ multiplied by each other ${\displaystyle 2}$ times.

The factor for ${\displaystyle b^1}$ is ${\displaystyle b}$ itself.

The factors for ${\displaystyle b^2}$ are ${\displaystyle b\cdot b}$, which is ${\displaystyle b}$ multiplied by each other ${\displaystyle 2}$ times.

The LCM of ${\displaystyle b^2,b^1,b^2}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

Multiply ${\displaystyle b}$ by ${\displaystyle b}$.

The LCM for ${\displaystyle 6b^2,6b,b^2}$ is the numeric part ${\displaystyle 6}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{6b^2}+\frac{1}{6b}=\frac{1}{b^2}}$ by ${\displaystyle 6b^2}$.

Simplify the left side.

Simplify the right side.

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

Subtract ${\displaystyle 1}$ from ${\displaystyle 6}$.