Find the Domain f(x)=(4x^2)/(3x)+4 , g(x)=9/x , g(f(x))

Cancel the common factor.

Divide ${\displaystyle x}$ by ${\displaystyle 1}$.

Factor ${\displaystyle x}$ out of ${\displaystyle 4x^2}$.

Factor ${\displaystyle x}$ out of ${\displaystyle 3x}$.

Cancel the common factor.

Rewrite the expression.

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

Since ${\displaystyle 3,1,1}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 3,1,1}$ then find LCM for the variable part .

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

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Since ${\displaystyle 3}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 3}$.

${\displaystyle 3}$ is a prime number

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

Not prime

The LCM of ${\displaystyle 3,1,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

Multiply each term in ${\displaystyle \frac{4x}{3}+4=0}$ by ${\displaystyle 3}$ in order to remove all the denominators from the equation.

Simplify each term.

Multiply ${\displaystyle 0}$ by ${\displaystyle 3}$.

Subtract ${\displaystyle 12}$ from both sides of the equation.

Divide each term by ${\displaystyle 4}$ and simplify.