Solve for c 1/20+1/10+1/c=1/5

Subtract ${\displaystyle \frac{1}{20}}$ from both sides of the equation.

Subtract ${\displaystyle \frac{1}{10}}$ from both sides of the equation.

To write ${\displaystyle \frac{1}{5}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{4}{4}}$.

Write each expression with a common denominator of ${\displaystyle 20}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle 1}$ from ${\displaystyle 4}$.

To write ${\displaystyle -\frac{1}{10}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{2}{2}}$.

Write each expression with a common denominator of ${\displaystyle 20}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle 2}$ from ${\displaystyle 3}$.

Multiply each term by a factor of ${\displaystyle 1}$ that will equate all the denominators. In this case, all terms need a denominator of ${\displaystyle 20c}$. The ${\displaystyle \frac{1}{c}}$ expression needs to be multiplied by ${\displaystyle \frac{20}{20}}$ to make the denominator ${\displaystyle 20c}$. The ${\displaystyle \frac{1}{20}}$ expression needs to be multiplied by ${\displaystyle \frac{c}{c}}$ to make the denominator ${\displaystyle 20c}$.

Multiply the expression by a factor of ${\displaystyle 1}$ to create the least common denominator (LCD) of ${\displaystyle 20c}$.

Multiply ${\displaystyle 20}$ by ${\displaystyle 1}$.

Multiply the expression by a factor of ${\displaystyle 1}$ to create the least common denominator (LCD) of ${\displaystyle 20c}$.

Multiply ${\displaystyle c}$ by ${\displaystyle 1}$.