Question

Add the rational expressions to find the sum: a/x+b/y
A. ay+bx/xy
B. a+b/xy
C a+b/x+y
D. ax+by/x+y

Answer 1

To find the sum of the rational expressions \( \frac{a}{x} + \frac{b}{y} \), we will first need to find a common denominator. The common denominator for \( x \) and \( y \) is \( xy \).

We can express each fraction with the common denominator:

\[
\frac{a}{x} = \frac{a \cdot y}{x \cdot y} = \frac{ay}{xy}
\]

\[
\frac{b}{y} = \frac{b \cdot x}{y \cdot x} = \frac{bx}{xy}
\]

Now, we can add the two fractions:

\[
\frac{a}{x} + \frac{b}{y} = \frac{ay}{xy} + \frac{bx}{xy} = \frac{ay + bx}{xy}
\]

Therefore, the sum of the rational expressions is:

\[
\frac{ay + bx}{xy}
\]

Looking at the answer choices provided:

A. \( \frac{ay + bx}{xy} \)

B. \( \frac{a + b}{xy} \)

C. \( \frac{a + b}{x + y} \)

D. \( \frac{ax + by}{x + y} \)

The correct answer is:

**A. \( \frac{ay + bx}{xy} \)**