Solve for n 3/5=3/(5n)-1/5

Add ${\displaystyle \frac{1}{5}}$ to both sides of the equation.

Combine the numerators over the common denominator.

Add ${\displaystyle 3}$ and ${\displaystyle 1}$.

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

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

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

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

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

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

Multiply each term in ${\displaystyle \frac{3}{5n}=\frac{4}{5}}$ by ${\displaystyle 5n}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 4n=3}$.

Divide each term in ${\displaystyle 4n=3}$ by ${\displaystyle 4}$ and simplify.