MATH-removable discontinuity?

Question

in the case of a removable discontinuity explain how to effect the removal

Answer 1

Most removable discontinuities come from fractions where there's a factor in the denominator that matches a factor in the numerator. Canceling these factors is how you remove the discontinuity.
I can't think of another kind of removable continuity off the top of my head.

Answer 2

usually a function has a removable discontinuity where either the function isnt defined at some point OR where the limit of the function isnt the same as the value of the function

draw yourself a graph of a function say a parabola or something like x^3; erase one of the points and adjust its y-value ... you now have a removable discontinuity in your function

well now say you have a graph/function as above with a discontinuity at some point(s), remove the discontinuity by making the graph continuous at that point ... [that last remark sounds a bit circular doesnt it lol ]
informally speaking more or less you want the flow of the pencil as you draw the graph not to jump or lift off the paper to draw another point

more formally you want the lim f(x) x--->a to be the same as f(a)
[if a function isnt defined at a point it umm cant be continuous there :) sooo go ahead and define it then so the above condition is true ]

Answer 3

To "remove" a removable discontinuity, the algebraic expressions would cancel

For instance y = (x-2)(x+3) / (x-2) has a discontinuity at x=2

This discontinuity can be removed by cancelling the (x-2) terms