Question

Equations Solve the rational equation. If the equ (4)/(x+2)+(5)/(x+3)=(14x+7)/ˣ²+5x+6)

Answer 1

To solve the given rational equation, eliminate terms, clear the denominators, simplify, solve the resulting quadratic equation, and check the solutions.

Step-by-step explanation:

To solve the rational equation (4)/(x+2)+(5)/(x+3)=(14x+7)/(x^2+5x+6), we'll follow these steps:

1. Eliminate terms wherever possible to simplify the algebra.
2. Multiply both sides of the equation by (x+2)(x+3) to clear the denominators.
3. Simplify the equation.
4. After simplifying, we'll have a quadratic equation.
5. Set the quadratic equation equal to zero and solve for x by factoring or using the quadratic formula.
6. Check the solution(s) to see if they satisfy the original equation.