Solve for r 2/(r+3)+1/2=9/10

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 ${\displaystyle \frac{5}{5}}$.

Write each expression with a common denominator of ${\displaystyle 10}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle 5}$ from ${\displaystyle 9}$.

Cancel the common factor of ${\displaystyle 4}$ and ${\displaystyle 10}$.

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

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.

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

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

The factor for ${\displaystyle r+3}$ is ${\displaystyle r+3}$ itself.

The LCM of ${\displaystyle r+3}$ is the result of multiplying all factors the greatest number of times they occur in either term.

The Least Common Multiple ${\displaystyle \mathrm{LCM}}$ of some numbers is the smallest number that the numbers are factors of.

Multiply each term in ${\displaystyle \frac{2}{r+3}=\frac{2}{5}}$ by ${\displaystyle 5(r+3)}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 2r+6=10}$.

Move all terms not containing ${\displaystyle r}$ to the right side of the equation.

Divide each term in ${\displaystyle 2r=4}$ by ${\displaystyle 2}$ and simplify.