Question

select the correct answer.
which expression is equivalent to the difference shown?
\\(\frac{5x + 1}{5x} - \frac{4x + 1}{4x}\\)
\\(\bigcirc\\) a. \\(\frac{1}{10x}\\)
\\(\bigcirc\\) b. \\(\frac{x}{20}\\)
\\(\bigcirc\\) c. \\(\frac{9}{20x}\\)
\\(\bigcirc\\) d. \\(-\frac{1}{20x}\\)

Explanation:

Step1: Find a common denominator

The denominators are \(5x\) and \(4x\), so the least common denominator (LCD) is \(20x\). Rewrite each fraction with the LCD:
\(\frac{5x + 1}{5x}=\frac{(5x + 1)\times4}{5x\times4}=\frac{20x + 4}{20x}\)
\(\frac{4x + 1}{4x}=\frac{(4x + 1)\times5}{4x\times5}=\frac{20x + 5}{20x}\)

Step2: Subtract the fractions

Now subtract the two fractions:
\(\frac{20x + 4}{20x}-\frac{20x + 5}{20x}=\frac{(20x + 4)-(20x + 5)}{20x}\)
Simplify the numerator:
\((20x + 4)-(20x + 5)=20x + 4 - 20x - 5=-1\)
So the result is \(\frac{-1}{20x}=-\frac{1}{20x}\)

Answer:

D. \(-\frac{1}{20x}\)