Evaluating Limits: Understanding the Solution to a Challenging Calculus Problem

[NoLimits]

Hello, I am struggling with limits in my calculus course and would appreciate a bit of help. The question is:

$$\lim_{x→-6}\frac{x^2-8x+12}{x^2-x+30}$$
So far I have tried the factoring and substitution methods but have not managed to match the answers given by online equation solvers. For example, when using direct substitution I get an answer of 4/3, whereas mathway (online solver) says the answer is x²-8x+12. Would someone please explain how that answer is possible? I've looked around online but nothing I've found seems to help in my understanding.

 

[Mark44]

Hello, I am struggling with limits in my calculus course and would appreciate a bit of help. The question is:

$$\lim_{x→-6}\frac{x^2-8x+12}{x^2-x+30}$$
So far I have tried the factoring and substitution methods but have not managed to match the answers given by online equation solvers. For example, when using direct substitution I get an answer of 4/3, whereas mathway (online solver) says the answer is x²-8x+12. Would someone please explain how that answer is possible? I've looked around online but nothing I've found seems to help in my understanding.

I get a limit of 4/3 as well. There's no way that I can see that the limit could be what you say mathway gives.

 

[NoLimits]

Thanks, I was driving myself crazy trying to figure out what I did wrong.