(1) When solving a rational equation what is the first step we must always take? Illustrate using the example
2/w + 3/5 = 5/6 how you clear the rational equation of fractions.
(2) After solving a rational equation, why is it important to check your answer? How is this done? What happens if you are checking a solution for the rational expression and find that it makes one of the denominators in the expression equal to zero? Solve the example below to help explain your answer to these questions.
(x – 2)/(x2 + 3x – 10) – x/(x + 5) = 4
Show how you get the answers {-3.8, 2}, yet only one of them is a true solution.
2. Carpentry. By checking work records, a carpenter finds that Juanita can build a small shed in 12 hr. Anton can do the same job in 16 hr. How long would it take if they worked together? Show a complete, detailed solution.