Solve for x -7/4-9/x=(2x+9)/(4x)

Subtract ${\displaystyle \frac{-7}{4}}$ from both sides of the equation.

Simplify each term.

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.

Add ${\displaystyle 2}$ and ${\displaystyle 7}$.

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

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

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 ${\displaystyle x^1}$ is ${\displaystyle x}$ itself.

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

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

Multiply each term in ${\displaystyle -\frac{9}{x}=\frac{9}{4x}+\frac{9}{4}}$ by ${\displaystyle 4x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 9+9x=-36}$.

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

Divide each term in ${\displaystyle 9x=-45}$ by ${\displaystyle 9}$ and simplify.