Chapter 11.4, Problem 22PPE

To determine

The LCD of $\frac{2}{ab},\frac{a-b}{b^{2}c}$

Answer to Problem 22PPE

The LCD is $a{b}^{3}c$

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 $\frac{2}{ab},\frac{a-b}{b^{2}c}$ 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 $ab$ and $b^{2}c$ . 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 $a{b}^{3}c$

Thus, the LCD is $a{b}^{3}c$