Solve for x 3/(5x+10)=x/(x+2)

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle 10}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x+5\cdot 2}$.

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.

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

The factor for ${\displaystyle x+2}$ is ${\displaystyle x+2}$ itself.

The LCM of ${\displaystyle x+2,x+2}$ 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 ${\displaystyle \frac{3}{5(x+2)}=\frac{x}{x+2}}$ by ${\displaystyle 5(x+2)}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 5x=3}$.

Divide each term in ${\displaystyle 5x=3}$ by ${\displaystyle 5}$ and simplify.