Math Journal

Math Journal #1

Describe how you would determine the expression in one variable for the denominator of a rational expression if the restrictions on the variable are xЎЩ2, -3.

The way you would solve a rational expression is first, you would have to factor out the numerator and denominator if itЎЇs possible. Then youЎЇd have to remove any common factors. After that youЎЇd have to exclude the values that would make the denominator equal to zero because if you didnЎЇt then the expression wouldnЎЇt be true. So if you wanted to determine the expression for the denominator of a rational expression based on the fact that the restrictions on the variable are xЎЩ2, and -3, you would have to work backwards.

Considering that the restrictions on the variable are xЎЩ2, and -3, I figured out that the denominator had to be (x-2) (x+3) before you found out what the restrictions were. The next thing you would do is expand the brackets using FOIL or any of the other various methods. When you expand the bracket you get: x2 + 3x ЁC 2x ЁC 6. Then when you simplify it you would get x2 + x ЁC 6. So therefore, the expression is

You canЎЇt add a common factor because then the expression wouldnЎЇt make any sense. Eg. If this was the expression:

The answer would change if you added any number as a common factor. So this is how you know that the numerator is one. Because the numerator is one, this means that you donЎЇt have to reduce anything because there are no common factors.

So basically, the expression is the one I wrote before. I got this expression by working backwards. Like I said, using the restrictions I figured out what the denominator was before