A rational equation is an equation that contains one or more rational expressions. To solve a rational equation: 1.Find the LCM of the denominators. 2.Multiply EVERYTHING by the LCM (This clears the denominators) 3.Solve the equation. An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation.
Solve the equation. The LCM is x, so multiply everything by x. x 2 -18=3x Now solve like normal x 2 -3x + 18 = 0 (x -3)(x+6)=0 x = 3, -6 Check 3 or -6 to make sure they are not undefined values of the original problem. If they are undefined values, then they are an extraneous solution, and we don’t include them in the answer.
Solve each equation. The solution, x = 2 is an extraneous solution, so in this case, there are no solutions. All you need to write is no solution.