Question

algebra 2 362403 - 6 fy - 1
benchmark test 2
if $b = \frac{3}{x} + \frac{3}{y}$, what is the value of $\frac{1}{b}$?
a. $\frac{x + y}{3y + 3x}$
b. $\frac{3xy}{y + x}$
c. $\frac{xy}{3y + 3x}$
d. $\frac{xy}{3y + x}$

Explanation:

Step1: Combine fractions for $b$

Find common denominator $xy$:
$$b = \frac{3y}{xy} + \frac{3x}{xy} = \frac{3y + 3x}{xy}$$

Step2: Take reciprocal of $b$

Flip numerator and denominator:
$$\frac{1}{b} = \frac{xy}{3y + 3x}$$

Answer:

C. $\frac{xy}{3y + 3x}$