MHB Solving Limit as x approaches 3 using Multiplication and Division

[tmt1]

I have to solve this limit.

$$\lim_{{x}\to{3}} \frac{\sqrt{6x - 14} - \sqrt{x + 1}}{x -3}$$

Now, I think that by definition x - 3 is a divisor of the numerator, but how do I advance from here? Do I do long division?

 

[I like Serena]

I have to solve this limit.

$$\lim_{{x}\to{3}} \frac{\sqrt{6x - 14} - \sqrt{x + 1}}{x -3}$$

Now, I think that by definition x - 3 is a divisor of the numerator, but how do I advance from here? Do I do long division?

How about making the x - 3 in the numerator explicit?
What do you get if you multiply both numerator and denominator by $\sqrt{6x - 14} + \sqrt{x + 1}$?

 

[tmt1]

How about making the x - 3 in the numerator explicit?
What do you get if you multiply both numerator and denominator by $\sqrt{6x - 14} + \sqrt{x + 1}$?

Okay thanks, now I got it.