Solve for y 2+10/y=3/4

Subtract ${\displaystyle 2}$ from both sides of the equation.

To write ${\displaystyle -2}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{4}{4}}$.

Combine ${\displaystyle -2}$ and ${\displaystyle \frac{4}{4}}$.

Combine the numerators over the common denominator.

Simplify the numerator.

Move the negative in front of the fraction.

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

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

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

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

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

Multiply each term in ${\displaystyle \frac{10}{y}=-\frac{5}{4}}$ by ${\displaystyle 4y}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle -5y=40}$.

Divide each term in ${\displaystyle -5y=40}$ by ${\displaystyle -5}$ and simplify.