Chapter 11.4, Problem 19PPE

To determine

The LCD of $\frac{1}{z},\frac{3}{7z}$

Answer to Problem 19PPE

The LCD is $7z^2$

Explanation of Solution

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
• Multiply both sides of equations by LCD(least common denominator) of all denominators.
• Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order to find the LCD of $\frac{1}{z},\frac{3}{7z}$ we know that the LCD is the smallest number or expression which is divisible by all the denominators

So observe that the denominators of the fractions are $z$ and $7z$ . Since there is nothing common in both of them, so the Least Common Denominator which will be divisible by both the denominators will be product of both denominators that is $7z^2$

Thus, the LCD is $7z^2$