Hello:

I'm trying to evaluate this limit:

$
lim [(sqrt(7-x) - 2)/(sqrt(4-x)-1)]
x->3
$

but I'm having trouble getting started on this. I've tried rationalizing the numerator and denominator but doing that doesn't get me anywhere. Any thoughts??

2. $\dfrac{{\sqrt {7 - x} - 2}}{{\sqrt {4 - x} - 1}} = \dfrac{{\sqrt {4 - x} + 1}}{{\sqrt {7 - x} + 2}}$

That should work.

3. Yea, that works. So you inverted the fraction but what is the rational behind changing - to +? How does that happen??

4. Originally Posted by chili5
Yea, that works. So you inverted the fraction but what is the rational behind changing - to +? How does that happen??
Multiply $\frac{{\sqrt {7 - x} - 2}}
{{\sqrt {4 - x} - 1}}\left( {\frac{{\sqrt {7 - x} + 2}}
{{\sqrt {7 - x} + 2}}} \right)\left( {\frac{{\sqrt {4 - x} + 1}}
{{\sqrt {4 - x} + 1}}} \right)$