Simplify \(\frac{x(x + 1)^{\frac{1}{2}} - (x + 1)^{\frac{1}{2}}}{(x + 1)^{\frac{1}{2}}}\)
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Correct Answer: Option A
Explanation:
\(\frac{x}{(x + 1)}\) - \(\frac{\sqrt{(x + 1)}{\sqrt{x + 1}}\)
= \(\frac{x}{x + 1}\) - 1
\(\frac{x - x - 1}{x + 1}\) = \(\frac{-1}{x + 1}\)
\(\frac{x}{(x + 1)}\) - \(\frac{\sqrt{(x + 1)}{\sqrt{x + 1}}\)
= \(\frac{x}{x + 1}\) - 1
\(\frac{x - x - 1}{x + 1}\) = \(\frac{-1}{x + 1}\)