Example
Express each of the following as a single fraction in its simplest form.
(a)

Ask by Munoz Moran. in Singapore

Mar 30,2025

Question

Example Express each of the following as a single fraction in its simplest form. (a) $$ \frac{x}{4 y}+\frac{2 y}{3 x} $$

UpStudy AI · Accepted Answer

$$
\frac{x}{4y} + \frac{2y}{3x}
$$

1. Find the least common denominator (LCD) of $$4y$$ and $$3x$$. The LCD is $$12xy$$.

2. Rewrite each fraction with the LCD:
   - For $$\frac{x}{4y}$$, multiply the numerator and the denominator by $$3x$$:
     $$
     \frac{x}{4y} = \frac{x \cdot 3x}{4y \cdot 3x} = \frac{3x^2}{12xy}
     $$
   - For $$\frac{2y}{3x}$$, multiply the numerator and the denominator by $$4y$$:
     $$
     \frac{2y}{3x} = \frac{2y \cdot 4y}{3x \cdot 4y} = \frac{8y^2}{12xy}
     $$

3. Combine the fractions:
   $$
   \frac{3x^2}{12xy} + \frac{8y^2}{12xy} = \frac{3x^2 + 8y^2}{12xy}
   $$

Thus, the expression as a single fraction in simplest form is:
$$
\frac{3x^2 + 8y^2}{12xy}
$$
$$ \frac{3x^2 + 8y^2}{12xy} $$

Example
Express each of the following as a single fraction in its simplest form.
(a)

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