To solve the rational equation $$ \frac{5}{x-1}+\frac{3}{4}=\frac{1}{x} $$, how can expression $$ \frac{5}{x-1} $$ be rewritten using the least common denominator? a.) $$ \frac{20}{4(x-1)} $$ b.) $$ \frac{20 x}{4 x(x-1)} $$ c.) $$ \frac{5 x}{x(x-1)} $$ d.) $$ \frac{8}{(x-1)} $$ (1) (

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To rewrite the expression $$ \frac{5}{x-1} $$ using the **least common denominator (LCD)**, follow these steps:

1. **Identify the Denominators:**
   - $$ \frac{5}{x-1} $$ has a denominator of $$ x - 1 $$.
   - $$ \frac{3}{4} $$ has a denominator of $$ 4 $$.
   - $$ \frac{1}{x} $$ has a denominator of $$ x $$.

2. **Determine the LCD:**
   - The LCD must include each distinct denominator:
     $$
     \text{LCD} = 4 \times x \times (x - 1) = 4x(x - 1)
     $$

3. **Rewrite $$ \frac{5}{x-1} $$ with the LCD:**
   - Multiply both the numerator and the denominator of $$ \frac{5}{x-1} $$ by $$ 4x $$ to achieve the LCD:
     $$
     \frac{5}{x-1} = \frac{5 \times 4x}{(x-1) \times 4x} = \frac{20x}{4x(x-1)}
     $$

Therefore, the correct rewritten form using the LCD is:

**b.) $$ \frac{20 x}{4 x(x-1)} $$**
The expression $$ \frac{5}{x-1} $$ can be rewritten using the least common denominator as $$ \frac{20x}{4x(x-1)} $$.

To solve the rational equation \( \frac{5}{x-1}+\frac{3}{4}=\frac{1}{x} \), how can expression \( \frac{5}{x-1} \) be rewritten using the least common denominator? a.) \( \frac{20}{4(x-1)} \) b.) \( \frac{20 x}{4 x(x-1)} \) c.) \( \frac{5 x}{x(x-1)} \) d.) \( \frac{8}{(x-1)} \) (1) (

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