Math CentralQuandaries & Queries


Question from Janie, a student:

I have to State the excluded values for this equation and then solve, but not sure how to do this. Here is the problem

Hi Janie,

I think you missed a pair of parentheses and the expression should be (x+6)/(x+3) = (3)/(x+3)+2.

I'm going to look at a very similar expression


Excluded values are values of x that result in the expression producing something which is not a real number. In my expression a value of x = 2 makes the denominators equal to zero and hence the expression evaluates to something that is not a real number. For any other value of x the two sides of the equation yield real numbers. Thus the only excluded value is x = 2.

To solve the equation I would multiply both values by x - 2 to get

x + 1 = 3 + 5(x - 2)

which on simplification becomes

x = 2.

But for x = 2 is excluded so the equation has no solution. Sometimes we say that x = 2 is an extraneous solution.

This is why it's important to verify your answer when you solve an algebraic equation. If you missed the fact that x = 2 is an excluded value and solved the equation as I did you might think that x = 2 is a solution. An attempt at verification by substitution of x = 2 into the original equation shows that x = 2 is not a solution.

Now try your problem,

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