1. $$ \frac{3}{2 x}+\frac{5}{4 x y} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{3}{2x} + \frac{5}{4xy}
$$

**Step 1: Find a Common Denominator**

The denominators are $$2x$$ and $$4xy$$. The least common denominator (LCD) is $$4xy$$.

**Step 2: Rewrite Each Fraction with the LCD**

1. **First Fraction:**
   
   $$
   \frac{3}{2x} = \frac{3 \times 2y}{2x \times 2y} = \frac{6y}{4xy}
   $$
   
2. **Second Fraction:**

$$
   \frac{5}{4xy} \quad (\text{already has the LCD})
   $$

**Step 3: Add the Fractions**

$$
\frac{6y}{4xy} + \frac{5}{4xy} = \frac{6y + 5}{4xy}
$$

**Final Simplified Expression:**

$$
\frac{6y + 5}{4xy}
$$
$$ \frac{6y + 5}{4xy} $$

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