# Solve equation, containing rational expression, for a specific varible. Solving an equation, containing rational equations, for a specific variable. Here we’re given the equation T equals the fraction six U divide by the quantity of a B plus E And we have to solve for E. The directions for solving this proble is the same as solving any other equation that contains a rational or fractional expression. So I have a typo here, it should be containing rational expressions. Anyway, the first thing you wanna do is find your least common denominator. In this case you we only have one denominator so it’s really just that denominator. The econd step we want to do is take this LCD and multiply everything every term, both on the left and right, by this LCD. So if I have T equals the quantity 6U divided by the quantity B+E I will multiply both sides by this LCD. And I’m going to use parenthesis because I will have to distribute in orderr to get the final answer. If I multiply by the quantiy of B+E on the right hand side I can cancel out those two quantities because it’s really like dividing by 1 and then multiplying straight acrosss or cross multiplying On the left-hand-side, I’m going to the T inside to get TB +TE equals on the right-hand-side I’m left with 6U The next step find your E. and solve for it. In this case, I’ve got some multiplication here that I need to undo, and some addition here that I need to undo. So let’s do our order of operations backwards and let’s take TB+TE and undo by subtracting TB on both sides of our equation On the right hand side, the TB will cancel, leaving us with TE And on the right-hand-side I’ll rewrite the expressions since there’s nothing I can do to combine these terms because they have different variables to get just 6U-TB And then finally all I need to do again is get this E by itself and since I have a multiplication with a T attached to it I will divide everything, or both sides, by the letter T. I’m going to do it by each term, but you could do the entire expression – that’s fine. and after that I will cancel out the T variable on the left-hand-side and rewrite the answer which is E= 6u divided by T subtract, notice these Ts cancel out, and I’m left with B. And that is all.