Question

Find the LCD of the given rational equation x/x+4+x-1/x+2=3/x²+2x-8

Answer 1

Final answer:

The least common denominator (LCD) for the rational equation is
`\((x+4)(x+2)(x-2)\)`.

Step-by-step explanation:

To find the least common denominator (LCD) for the rational equation
`\((x)/(x+4) + (x-1)/(x+2) = (3)/(x^2+2x-8)\)`, we need to factor the denominators and identify the unique factors.

1. **Factorization of Denominators:**

-
`\(x+4\)` is already a linear factor.

-
`\(x+2\)` is already a linear factor.

- Factorizing
`\(x^2+2x-8\), we get \((x+4)(x-2)\)`.

2. **Identify Unique Factors:**

- The unique factors are
`\(x+4\), \(x+2\), and \(x-2\)`.

3. **Determine the LCD:**

- The LCD is the product of all unique factors raised to their highest powers.

- Therefore, the LCD is
`\((x+4)(x+2)(x-2)\)`.

So, the LCD for the given rational equation is
`\((x+4)(x+2)(x-2)\)`.