Solve for r 2/r+1/2=3/4

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

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

Write each expression with a common denominator of ${\displaystyle 4}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle 2}$ from ${\displaystyle 3}$.

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

Since ${\displaystyle r,4}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 1,4}$ then find LCM for the variable part ${\displaystyle r^1}$.

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

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

${\displaystyle 4}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 2}$.

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

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

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

The LCM for ${\displaystyle r,4}$ is the numeric part ${\displaystyle 4}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{2}{r}=\frac{1}{4}}$ by ${\displaystyle 4r}$.

Simplify the left side.

Simplify the right side.