Calculus homework help, please

Let f(x)= (2x^2 + 5x - 18) / (x - 2)
Show that f(x) has a removable discontinuity at x=2 and determine what value for f(2) would make f(x) continuous at x=2.
Must define f(2)=?

How do I do this problem? Can't figure out how to set it up.

And I'm sure this one is similar:
let f(x)=
x^2 + 10x + 30, if x< - 5
-2, if x= - 5
-x^2 - 10x - 20, if x> - 5

Show that f(x) has a removable discontinuity at x= - 5 and determine what value for f( - 5) would make f (x) continuous at x= - 5.
Must redefine f( - 5)=?

I don't want the answers; that won't help me at all. I want to know how to do them. Thanks!

(2x^2 + 5x - 18) / (x - 2)
= (x-2)(2x+9)/(x-2)
= 2x+9
if x=2, 2x+9=13

define f(2)=13 to make it continuous

--------------------------------------…
lim x-->-5- f(x) = (-5)^2 +10(-5) + 30 = 5
lim x-->-5+ f(x) = -(-5)^2 -10(-5) -20 = 5
Since the left and right side limits are equal, lim x-->-5 f(x) exists and equal to 5.
In order for x to be continuous at x=-5, f(x) must be equal to 5
Redefine f(-5) = 5

f(x) has a removable discontinuity at x=2 implies that x-2 is a common factor of the rational function.

Try it!

No matter what the exercise says, f(2) does not exist!. the discontinuity removes the point (2, 13)