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

Simplify expression inside parentheses: Simplify the expression inside the parentheses. We have the expression ((1+(x)/(y)))/(((x)/(y))). To simplify, we first look at the numerator, which is 1 + (x/y). There is nothing to simplify here, so we move on to the next step.Divide numerator by denominator: Divide the numerator by the denominator. Now we divide the entire numerator by the denominator. In other words, we are looking for the result of (1 + (x/y)) / (x/y). To divide by a fraction, we multiply by its reciprocal. So, we multiply (1 + (x/y)) by (y/x).Perform the multiplication: Perform the multiplication. Multiplying (1 + (x/y)) by (y/x) gives us (y/x) + (x/y) * (y/x). The term (x/y) * (y/x) simplifies to 1 because the y's and x's cancel out.Combine the terms: Combine the terms. After simplification, we have (y/x) + 1. This can be rewritten as (y + x)/x because we are adding 1 (which is x/x) to y/x.Check the answer choices: Check the answer choices. We need to find the expression that matches our result, which is (y + x)/x. Looking at the answer choices, we see that (C) (y+x)/(x) is the correct match.

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

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

\frac{x}{y}

\newline

(C)

\frac{y+x}{x}

\newline

(D)

\frac{y}{x}

Simplify expression inside parentheses: Simplify the expression inside the parentheses. $\newline$ We have the expression $\left(\frac{1+(x)/(y)}{(x)/(y)}\right)$ . To simplify, we first look at the numerator, which is $1 + \frac{x}{y}$ . There is nothing to simplify here, so we move on to the next step.
Divide numerator by denominator: Divide the numerator by the denominator. $\newline$ Now we divide the entire numerator by the denominator. In other words, we are looking for the result of $(1 + (x/y)) / (x/y)$ . To divide by a fraction, we multiply by its reciprocal. So, we multiply $(1 + (x/y))$ by $(y/x)$ .
Perform the multiplication: Perform the multiplication. $\newline$ Multiplying $(1 + (\frac{x}{y}))$ by $(\frac{y}{x})$ gives us $(\frac{y}{x}) + (\frac{x}{y}) \times (\frac{y}{x})$ . The term $(\frac{x}{y}) \times (\frac{y}{x})$ simplifies to $1$ because the y's and x's cancel out.
Combine the terms: Combine the terms. $\newline$ After simplification, we have $(\frac{y}{x}) + 1$ . This can be rewritten as $(\frac{y + x}{x})$ because we are adding $1$ (which is $\frac{x}{x}$ ) to $\frac{y}{x}$ .
Check the answer choices: Check the answer choices. $\newline$ We need to find the expression that matches our result, which is $(y + x)/x$ . Looking at the answer choices, we see that (C) $(y+x)/(x)$ is the correct match.