How Do You Solve a Rational Equation With an Extraneous Solution?

1. Since our fractions have different denominators, we will need to find a common denominator in order to add them
1. We need to exclude all the values for t that will make any of our denominators equal to 0
1. We need to find a least common denominator so that we can add the fractions
1. We can multiply each fraction by something over itself to give them all the least common denominator
2. Remember, anything over itself is just 1, so we're not changing the values of the fractions
1. Now that we have common denominators, we can just add the numerators
1. Since the denominators are equal, the numerators must be equal as well
2. So we can just set the numerators equal to each other to make an equation we can solve for t
1. The answer we got for t, -3, is one of our excluded values
2. Since -3 would make at least one of the denominators 0 in our original equation, it cannot be a solution
3. Since we have no other solutions besides -3, this equation has no solution

Solve for t: 1/(t+3)+2/t=-3/t(t+3)