## hpfan101 one year ago What is the limit as x approaches 2 of the function (1/x - 1/3)/(x-3)? The fractions part of the problem made me confused and get the wrong answer.

1. hpfan101

$\lim_{x \rightarrow 3} (\frac{ 1 }{ x } - \frac{ 1 }{ 3 })/(x-3)$

2. jdoe0001

what would you get for.. say $$\bf \cfrac{1}{x}-\cfrac{1}{3}?$$

3. hpfan101

You'd get 0 when you subsitute 3 for x.

4. jdoe0001

well.. I meant the numerator only :)

5. hpfan101

Oh ok. :D

6. hpfan101

The only thing I don't get is that I got 0 both in the numerator and the denominator. Not sure what to do next.

7. jdoe0001

right... one sec bear in mind that $$\bf a-b \iff -(b-a)$$ one sec

8. hpfan101

Ok

9. jdoe0001

$$\bf \lim\limits_{x\to 3}\ \cfrac{\frac{1}{x}-\frac{1}{3}}{x-3} \\ \quad \\ \cfrac{\frac{3-x}{3x}}{x-3}\implies \cfrac{\frac{3-x}{3x}}{\frac{x-3}{1}}\implies \cfrac{3-x}{3x}\cdot \cfrac{1}{x-3} \\ \quad \\ \cfrac{3-x}{3x(x-3)}\implies \cfrac{{\color{brown}{ -\cancel{(x-3)}}}}{3x\cancel{(x-3)}}$$

10. hpfan101

Oh, now I see what I was supposed to do! Thank you very much!

11. jdoe0001

yw