Solve for x 1/7+1/x=1/5

Subtract ${\displaystyle \frac{1}{7}}$ from both sides of the equation.

To write ${\displaystyle \frac{1}{5}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{7}{7}}$.

To write ${\displaystyle -\frac{1}{7}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{5}{5}}$.

Write each expression with a common denominator of ${\displaystyle 35}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle 5}$ from ${\displaystyle 7}$.

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

Since ${\displaystyle x,35}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 1,35}$ 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.

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

${\displaystyle 35}$ has factors of ${\displaystyle 5}$ and ${\displaystyle 7}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 7}$.

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 ${\displaystyle x,35}$ is the numeric part ${\displaystyle 35}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{x}=\frac{2}{35}}$ by ${\displaystyle 35x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 2x=35}$.

Divide each term in ${\displaystyle 2x=35}$ by ${\displaystyle 2}$ and simplify.