Question

What reasons justify a solution to a rational equation?

Answer 1

@myininaya

Answer 2

@Elsa213

Answer 3

A "rational expression" consists of a polynomial of a variable (such as x) divided by another polynomial. So you might have something like this:

x2 + 5x + 4
f(x) = ------------------
x2 + 9x + 14

Discontinuities occur when the denominator is 0. That's because you can't divide by 0, so the function isn't defined when the denominator is 0. There are a number of reasons why a function can be "discontinuous" at a specific value of x, but a common one is when it isn't defined at all for that value of x.

The zeros of a rational expression are the same as the zeros of the numerator (since 0 divided by anything is still 0), EXCEPT that you have to exclude any value that is also a zero of the denominator. That's because you'd have 0/0, and that's not defined either.


As for what reasons might lead you to want to solve such an equation, I'm not sure I can say with any specificity. If you're solving a problem and that's the way the math works out, then that's what you've got. I'm not aware of specific types of problems that lead to a rational expression, but someone else might be.

Answer 4

Thank you. :)