Question

select the correct answer.
a jet flew from new york to los angeles, a distance of 4,200 kilometers. then it completed the return trip. the speed for the return trip was 100 kilometers/hour faster than the outbound speed. this expression, where x is the speed for the outbound trip, represents the situation.
\\(\frac{4200}{x} + \frac{4200}{x + 100}\\)
which expression could be a step in rewriting this sum?
a. \\(\frac{4200(x + 100)}{x(x + 100)} + \frac{4200x}{x(x + 100)}\\)
b. \\(\frac{4200(x + 100)}{(x + 100)} + \frac{4200x}{x}\\)
c. \\(\frac{8400(x + 100)}{x(x + 100)}\\)
d. \\(\frac{4200}{x + (x + 100)} + \frac{4200}{x + (x + 100)}\\)

Explanation:

Step1: Find common denominator

To add \(\frac{4200}{x}\) and \(\frac{4200}{x + 100}\), the common denominator is \(x(x + 100)\).

Step2: Rewrite fractions

Rewrite each fraction with the common denominator: \(\frac{4200(x + 100)}{x(x + 100)}+\frac{4200x}{x(x + 100)}\) (this matches option A's first term and a similar second term structure when considering the sum steps). Wait, re - evaluating: Wait, the original sum is \(\frac{4200}{x}+\frac{4200}{x + 100}\). To get a common denominator of \(x(x + 100)\), we multiply the first fraction's numerator and denominator by \((x + 100)\) and the second fraction's numerator and denominator by \(x\). So \(\frac{4200(x + 100)}{x(x + 100)}+\frac{4200x}{x(x + 100)}\), which is the same as option A: \(\frac{4200(x + 100)}{x(x + 100)}+\frac{4200x}{x(x + 100)}\) (the option A is \(\frac{4200(x + 100)}{x(x + 100)}+\frac{4200x}{x(x + 100)}\) when we check the expression).

Answer:

A. \(\frac{4200(x + 100)}{x(x + 100)}+\frac{4200x}{x(x + 100)}\)