# Solve for Variables to Find Continuity

Hypnos_16

## Homework Statement

y = 1 - 9x-2 / 1 - 3x-1 if x ≠ 3
y = a if x = 3

find the value of "a" that makes the graph Continuous at x = 3

n/a

## The Attempt at a Solution

I'm really not sure here, i think i must've missed this class or something, cause i just can't figure this out at all. I have two others to do too and i can't get any of them.

Homework Helper
Gold Member
You might want to compute

$$\lim_{x\rightarrow 3} \frac{1-\frac{9}{x^2}}{1-\frac{3}{x}}$$

and sketch the function around $$x=3$$ to see how it behaves.

Hypnos_16
Alright, i'll try that, is there also a way to solve it mathematically? Because i don't know what way he's looking for in the question.

Homework Helper
What fzero suggests was "mathematical"! However:
The first thing I would do is multiply both numerator and denominator by $x^2$ to get
$$\frac{x^2- 9}{x^3- 3x}= \frac{(x- 3)(x+3)}{x(x-3)}$$
which is the same as $\frac{x+ 3}{x}$ as long as x is not equal to 3. What is that when x= 3?