Solve the Rational Equation for a (a+1)/(5a)-1/a=1

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

Since ${\displaystyle 5a,a,1}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 5,1,1}$ then find LCM for the variable part ${\displaystyle a^1,a^1}$.

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

Since ${\displaystyle 5}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 5}$.

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

The LCM of ${\displaystyle 5,1,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

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

The LCM for ${\displaystyle 5a,a,1}$ is the numeric part ${\displaystyle 5}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{a+1}{5a}-\frac{1}{a}=1}$ by ${\displaystyle 5a}$.

Simplify the left side.

Simplify the right side.

Move all terms containing ${\displaystyle a}$ to the left side of the equation.

Add ${\displaystyle 4}$ to both sides of the equation.

Divide each term in ${\displaystyle -4a=4}$ by ${\displaystyle -4}$ and simplify.