Chapter 11.4, Problem 20PPE

To determine

The LCD of $\frac{8}{5b},\frac{12}{7b^{3}c}$

Answer to Problem 20PPE

The LCD is $35b^{4}c$

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 $\frac{8}{5b},\frac{12}{7b^{3}c}$ 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 $5b$ and $7b^{3}c$ . 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 $35b^{4}c$

Thus, the LCD is $35b^{4}c$