Final answer:
To solve the given rational equation, we find the least common denominator, eliminate fractions by multiplying through, simplify, and solve for y while checking for restrictions on the variable.
Step-by-step explanation:
Solving Rational Equations
First, we need to address and correct the equation you've provided because there seems to be a typo in it. Assuming the equation is: (25/(y+4)) + (10/(y+2)) = (30/(y+2)) - (5/(y2+6y+8)). We will solve it step by step. A critical step in solving rational equations is to find a common denominator.
- Identify the least common denominator (LCD).
- Multiply both sides of the equation by the LCD to eliminate the fractions.
- Simplify the resulting equation and solve for y.
- Check the solutions in the original equation to ensure they don't result in a division by zero.
Solutions for y are typically found by first clearing the denominators and then solving the resulting polynomial equation. For a more precise solution, factoring, the quadratic formula, or other algebraic methods may be used.