Given:
Quantity A: \((\frac{1}{2} + \frac{1}{m}) \times (m+2)\)

Quantity B: \(\frac{(m+2)^2}{2m}\)



why solve this way when you can simply do addition to the first term and get the same quantity as B?

Is I am missing something here?
Use FOIL to expand and simplify both quantities:
Quantity A: \(\frac{m}{2} + 2 + \frac{2}{m}\)

Quantity B: \(\frac{m^2+4m+4}{2m}\)


Multiply both quantities by 2 to get:
Quantity A: \(m + 4 + \frac{4}{m}\)

Quantity B: \(\frac{m^2+4m+4}{m}\)


USEFUL FRACTION PROPERTY: \(\frac{a+b+c}{d}=\frac{a}{d}+\frac{b}{d}+\frac{c}{d}\)


Apply the above property to Quantity B to get:
Quantity A: \(m + 4 + \frac{4}{m}\)

Quantity B: \(\frac{m^2}{m}+\frac{4m}{m}+\frac{4}{m}\)


Simplify Quantity B to get:
Quantity A: \(m + 4 + \frac{4}{m}\)

Quantity B: \(m+4+\frac{4}{m}\)

Answer: C

Cheers,
Brent

\(m \neq 0\)

Quantity A	Quantity B
\((\frac{1}{2} + \frac{1}{m}) \times (m+2)\)	\(\frac{(m+2)^2}{2m}\)

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.