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Which of the following expressions is equivalent to (((2)/(x+y)))/(((x+y)/(2))) ? Choose 1 answer: (A) x+y (B) 1 (c) (4)/((x+y)^(2)) (D) (x+y)/(2)

Which of the following expressions is equivalent to (2x+y)(x+y2) \frac{\left(\frac{2}{x+y}\right)}{\left(\frac{x+y}{2}\right)} ?\newlineChoose 11 answer:\newline(A) x+y x+y \newline(B) 11\newline(C) 4(x+y)2 \frac{4}{(x+y)^{2}} \newline(D) x+y2 \frac{x+y}{2}

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Full solution

Q. Which of the following expressions is equivalent to (2x+y)(x+y2) \frac{\left(\frac{2}{x+y}\right)}{\left(\frac{x+y}{2}\right)} ?\newlineChoose 11 answer:\newline(A) x+y x+y \newline(B) 11\newline(C) 4(x+y)2 \frac{4}{(x+y)^{2}} \newline(D) x+y2 \frac{x+y}{2}
  1. Rephrasing the complex fraction: First, let's rephrase the ＂What is the equivalent expression for the given complex fraction?＂
  2. Multiplying by the reciprocal of the denominator: Now, let's simplify the given expression step by step. We have the complex fraction:\newline2x+yx+y2\frac{\frac{2}{x+y}}{\frac{x+y}{2}}\newlineTo simplify a complex fraction, we can multiply the numerator and the denominator by the reciprocal of the denominator. In this case, the reciprocal of x+y2\frac{x+y}{2} is 2x+y\frac{2}{x+y}.
  3. Simplifying the numerator: Now, let's multiply the numerator and the denominator by the reciprocal of the denominator:\newline(2x+y)×2x+y(\frac{2}{x+y}) \times \frac{2}{x+y} for the numerator and\newline(x+y2)×2x+y\left(\frac{x+y}{2}\right) \times \frac{2}{x+y} for the denominator.
  4. Simplifying the denominator: Simplifying the numerator:\newline(2x+y)×(2x+y)=2×2(x+y)×(x+y)=4(x+y)2(\frac{2}{x+y}) \times (\frac{2}{x+y}) = \frac{2 \times 2}{(x+y) \times (x+y)} = \frac{4}{(x+y)^2}
  5. Obtaining the simplified fraction: Simplifying the denominator: (x+y2)⋅(2x+y)=x+yx+y⋅22=1⋅1=1\left(\frac{x+y}{2}\right) \cdot \left(\frac{2}{x+y}\right) = \frac{x+y}{x+y} \cdot \frac{2}{2} = 1 \cdot 1 = 1
  6. Obtaining the simplified fraction: Simplifying the denominator:\newline(x+y2)⋅(2x+y)=x+yx+y⋅22=1⋅1=1(\frac{x+y}{2}) \cdot (\frac{2}{x+y}) = \frac{x+y}{x+y} \cdot \frac{2}{2} = 1 \cdot 1 = 1Now we have the simplified fraction:\newline4((x+y)2)/1\frac{4}{((x+y)^2)} / 1\newlineWhen we divide anything by 11, the value remains unchanged. So, the simplified expression is:\newline4((x+y)2)\frac{4}{((x+y)^2)}

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