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)

Rephrasing the complex fraction: First, let's rephrase the ＂What is the equivalent expression for the given complex fraction?＂Multiplying by the reciprocal of the denominator: Now, let's simplify the given expression step by step. We have the complex fraction: (((2)/(x+y)))/(((x+y)/(2))) To 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+y)/(2)) is (2/(x+y)).Simplifying the numerator: Now, let's multiply the numerator and the denominator by the reciprocal of the denominator: (2/(x+y)) * (2/(x+y)) for the numerator and ((x+y)/2) * (2/(x+y)) for the denominator.Simplifying the denominator: Simplifying the numerator: (2/(x+y)) * (2/(x+y)) = (2*2)/((x+y)*(x+y)) = 4/((x+y)^2)Obtaining the simplified fraction: Simplifying the denominator: ((x+y)/2) * (2/(x+y)) = (x+y)/(x+y) * 2/2 = 1 * 1 = 1Now we have the simplified fraction: (4/((x+y)^2)) / 1 When we divide anything by 1, the value remains unchanged. So, the simplified expression is: 4/((x+y)^2)

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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 $\frac{\left(\frac{2}{x+y}\right)}{\left(\frac{x+y}{2}\right)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $x+y$ $\newline$ (B) $1$ $\newline$ (C) $\frac{4}{(x+y)^{2}}$ $\newline$ (D) $\frac{x+y}{2}$

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Algebra 1

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Q. Which of the following expressions is equivalent to

\frac{\left(\frac{2}{x+y}\right)}{\left(\frac{x+y}{2}\right)}

\newline

Choose

1

answer:

\newline

(A)

x+y

\newline

(B)

1

\newline

(C)

\frac{4}{(x+y)^{2}}

\newline

(D)

\frac{x+y}{2}

Rephrasing the complex fraction: First, let's rephrase the ＂What is the equivalent expression for the given complex fraction?＂
Multiplying by the reciprocal of the denominator: Now, let's simplify the given expression step by step. We have the complex fraction: $\newline$ $\frac{\frac{2}{x+y}}{\frac{x+y}{2}}$ $\newline$ To simplify a complex fraction, we can multiply the numerator and the denominator by the reciprocal of the denominator. In this case, the reciprocal of $\frac{x+y}{2}$ is $\frac{2}{x+y}$ .
Simplifying the numerator: Now, let's multiply the numerator and the denominator by the reciprocal of the denominator: $\newline$ $(\frac{2}{x+y}) \times \frac{2}{x+y}$ for the numerator and $\newline$ $\left(\frac{x+y}{2}\right) \times \frac{2}{x+y}$ for the denominator.
Simplifying the denominator: Simplifying the numerator: $\newline$ $(\frac{2}{x+y}) \times (\frac{2}{x+y}) = \frac{2 \times 2}{(x+y) \times (x+y)} = \frac{4}{(x+y)^2}$
Obtaining the simplified fraction: Simplifying the denominator: $\left(\frac{x+y}{2}\right) \cdot \left(\frac{2}{x+y}\right) = \frac{x+y}{x+y} \cdot \frac{2}{2} = 1 \cdot 1 = 1$
Obtaining the simplified fraction: Simplifying the denominator: $\newline$ $(\frac{x+y}{2}) \cdot (\frac{2}{x+y}) = \frac{x+y}{x+y} \cdot \frac{2}{2} = 1 \cdot 1 = 1$ Now we have the simplified fraction: $\newline$ $\frac{4}{((x+y)^2)} / 1$ $\newline$ When we divide anything by $1$ , the value remains unchanged. So, the simplified expression is: $\newline$ $\frac{4}{((x+y)^2)}$