In high school math, non-permissible values become important. Yet, they root back to elementary school:<\/p>\n
“You can’t divide by zero,” uttered in metallic timbre, is recalled by many from then.<\/p>\n
A rational expression is defined to be<\/p>\n
polynomial\/polynomial<\/p>\n
an example being<\/p>\n
(2x-5)\/(x2<\/sup>-x-12)<\/p>\n Fundamentally, such an expression is division, since by definition,<\/p>\n a\/b = a\u00f7b<\/p>\n Accepting that we can’t divide by zero, it follows that the bottom of the fraction mustn’t be zero. The bottom of the fraction is also called the denominator:<\/p>\n numerator\/denominator<\/p>\n We arrive at the condition that the denominator mustn’t equal zero. Then, the values that would make it zero are the non-permissible values<\/em>.<\/p>\n Example 1:<\/p>\n Give the non-permissible values of (2x+4)\/(x2<\/sup>+3x)<\/p>\n Solution:<\/p>\n First, we factor the denominator:<\/p>\n (2x+4)\/(x(x+3))<\/p>\n Now we observe that if x=0 or x=-3, the denominator will be zero. Therefore, 0 and -3 are the non-permissible values.<\/p>\n Example 2:<\/p>\n Give the non-permissible values of (x+5)\/(x2<\/sup>-25)<\/p>\n Solution:<\/p>\n Once again, we factor the denominator:<\/p>\n (x+5)\/((x+5)(x-5))<\/p>\n We see that the denominator will be zero if x=-5 or if x=5. Therefore, -5 and 5 are the non-permissible values.<\/p>\n Some people ask, Can’t you cancel the (x+5) top and bottom, to arrive at<\/p>\n 1\/(x-5) ?<\/p>\n Since that cancellation is actually division, you can only do so if x+5\u22600. Therefore, potential cancellation does not change non-permissible values<\/em>.<\/p>\n This is a first look at non-permissible values. I’ll probably do a follow-up.<\/p>\n HTH:)<\/p>\n