How Do You Solve a Rational Equation With Binomials in the Denominator?

We need to exclude all the values for t that would make any of the denominators equal 0
We need to find the least common denominator so that we can add the fractions

1. Since we have variables in the denominators of fractions, we need to find excluded values for t
2. Also, our fractions don't have common denominators
3. So we'll need to find a least common denominator
1. Excluded values are the values for t that would make one of the denominators equal 0
2. Since you can't have 0 in the denominator, t cannot equal any of these values
1. Since our fractions have different denominators, we need to find a least common denominator before we can add
1. In order to get common denominators for all of our fractions, we need to multiply each one by something over itself
2. Remember, anything over itself is just 1, so we're not actually changing the value of the fraction
1. Now that our fractions 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 solve for t
3. Since t does not equal either of our excluded values, -3 or 0, we can keep it as our answer
1. Plug 1 in for t into the original equation to make sure we get a true statement
1. Multiply 2/1 by 4/4 to get a common denominator of 4

Solve for t: 1/(t+3)+2/t=9/(t+3)