Solve for x -1+5/4=-5/(4x)

Move the negative in front of the fraction.

To write ${\displaystyle -1}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{4}{4}}$.

Combine ${\displaystyle -1}$ and ${\displaystyle \frac{4}{4}}$.

Combine the numerators over the common denominator.

Simplify the numerator.

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

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

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

${\displaystyle 4}$ 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 ${\displaystyle x^1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

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

Multiply each term in ${\displaystyle -\frac{5}{4x}=\frac{1}{4}}$ by ${\displaystyle 4x}$.

Simplify the left side.

Simplify the right side.