Chapter 11.4, Problem 24PPE

To determine

The LCD of $\frac{1}{k},\frac{3}{k^2-2}$

Answer to Problem 24PPE

The LCD is $k\left(k^2-2\right)$ .

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 $\frac{1}{k},\frac{3}{k^2-2}$ 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 $k$ and $k^2-2$ . 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 $k\left(k^2-2\right)$

Thus, the LCD is $k\left(k^2-2\right)$