Question

How do I solve `f(x)=(2x+5)/(x-1)` on a TI-84?

Answer 1

You can solve it by simply plugging it into your `y=` button, and finding the zeroes using 2nd->Calc->Zero (in this case it is `-2.5`).

However, you can considerably reduce the chances of you punching in something wrong into the calculator by considering this simple property: the zeroes of rational functions are the zeroes of the numerator. Basically, you can solve the equation by plugging in the numerator alone, and getting it's zeroes.

This is because if you solve it by algebra, you wind up with this:

`(2x+5)/(x-1) = 0` (`x` intercept implies that `y=0`)

`(2x+5)/(x-1)*(x-1) = 0(x-1)`

`2x+5 = 0`

Hence shown, the denominator of your rational function has no real impact on what your function's zeroes will be. You can even see this on a graph:

Hope that helps :)