Find the least common denominator of \( \frac{2 x}{x^{2}+x-20} \) and \( \frac{3 x}{x^{2}+4 x-5} \).

To find the least common denominator (LCD) of the fractions \( \frac{2 x}{x^{2}+x-20} \) and \( \frac{3 x}{x^{2}+4 x-5} \), we first need to factor the denominators of both fractions. 1. **Factor the first denominator**: \[ x^{2} + x - 20 \] We look for two numbers that multiply to \(-20\) and add to \(1\). The numbers \(5\) and \(-4\) work because: \[ 5 \cdot (-4) = -20 \quad \text{and} \quad 5 + (-4) = 1 \] Therefore, we can factor it as: \[ x^{2} + x - 20 = (x + 5)(x - 4) \] 2. **Factor the second denominator**: \[ x^{2} + 4x - 5 \] We need two numbers that multiply to \(-5\) and add to \(4\). The numbers \(5\) and \(-1\) work since: \[ 5 \cdot (-1) = -5 \quad \text{and} \quad 5 + (-1) = 4 \] Thus, we can factor this as: \[ x^{2} + 4x - 5 = (x + 5)(x - 1) \] 3. **Identify the least common denominator**: The denominators of the fractions are: \[ (x + 5)(x - 4) \quad \text{and} \quad (x + 5)(x - 1) \] The LCD will take the highest power of each factor present in both denominators. The factors are \(x + 5\), \(x - 4\), and \(x - 1\). Therefore, the least common denominator (LCD) is: \[ (x + 5)(x - 4)(x - 1) \] Thus, the least common denominator of \( \frac{2 x}{x^{2}+x-20} \) and \( \frac{3 x}{x^{2}+4 x-5} \) is \(\boxed{(x + 5)(x - 4)(x - 1)}\).