Which of the following expressions is equivalent to (((x)/(y)+1))/(((x)/(y)-1)) ? Choose 1 answer: (A) (x+y)/(x-y) (B) (1)/(x+y) (C) (1)/(x-y) (D) (x+y)/(y-x)

Simplify terms separately: Simplify the numerator and denominator separately by finding a common denominator. The numerator is (x/y) + 1, which can be written as (x/y) + (y/y) to have a common denominator. Similarly, the denominator is (x/y) - 1, which can be written as (x/y) - (y/y).Combine terms: Combine the terms in the numerator and the denominator. Numerator: (x/y) + (y/y) = (x+y)/y Denominator: (x/y) - (y/y) = (x-y)/yWrite original expression: Write the original expression with the simplified numerator and denominator. The expression now looks like this: ((x+y)/y) / ((x-y)/y)Multiply by reciprocal: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator. This is equivalent to ((x+y)/y) * (y/(x-y))Cancel common factors: Cancel out the common factors in the numerator and denominator. The 'y' in the numerator and the 'y' in the denominator cancel each other out. This leaves us with (x+y)/(x-y)Compare with answer choices: Compare the simplified expression with the answer choices. The simplified expression (x+y)/(x-y) matches with answer choice (A).

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Math Problems

Algebra 1

Identify equivalent linear expressions

Full solution

Q. Which of the following expressions is equivalent to

\frac{\left(\frac{x}{y}+1\right)}{\left(\frac{x}{y}-1\right)}

\newline

Choose

1

answer:

\newline

(A)

\frac{x+y}{x-y}

\newline

(B)

\frac{1}{x+y}

\newline

(C)

\frac{1}{x-y}

\newline

\frac{x+y}{y-x}

Simplify terms separately: Simplify the numerator and denominator separately by finding a common denominator. $\newline$ The numerator is $(\frac{x}{y}) + 1$ , which can be written as $(\frac{x}{y}) + (\frac{y}{y})$ to have a common denominator. $\newline$ Similarly, the denominator is $(\frac{x}{y}) - 1$ , which can be written as $(\frac{x}{y}) - (\frac{y}{y})$ .
Combine terms: Combine the terms in the numerator and the denominator. $\newline$ Numerator: $(\frac{x}{y}) + (\frac{y}{y}) = \frac{x+y}{y}$ $\newline$ Denominator: $(\frac{x}{y}) - (\frac{y}{y}) = \frac{x-y}{y}$
Write original expression: Write the original expression with the simplified numerator and denominator. $\newline$ The expression now looks like this: $\left(\frac{x+y}{y}\right) / \left(\frac{x-y}{y}\right)$
Multiply by reciprocal: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator. $\newline$ This is equivalent to $\left(\frac{x+y}{y}\right) \times \left(\frac{y}{x-y}\right)$
Cancel common factors: Cancel out the common factors in the numerator and denominator. $\newline$ The ' $y$ ' in the numerator and the ' $y$ ' in the denominator cancel each other out. $\newline$ This leaves us with $(x+y)/(x-y)$
Compare with answer choices: Compare the simplified expression with the answer choices. $\newline$ The simplified expression $(x+y)/(x-y)$ matches with answer choice (A).