# Thread: Complete the operation and simplify

1. ## Complete the operation and simplify

Couldn't get the LaTex to work, so here it is:

(3+1/x) / (3-1/x)

2. $$\dfrac{3+\frac{1}{x}}{3-\frac{1}{x}}$$ gives $\dfrac{3+\frac{1}{x}}{3-\frac{1}{x}}$

3. Originally Posted by fcabanski
Couldn't get the LaTex to work, so here it is:

(3+1/x) / (3-1/x)
multiply numerator and denominator by x.

4. $\displaystyle \frac{3 + \frac{1}{x}}{3 - \frac{1}{x}} = \frac{\frac{3x + 1}{x}}{\frac{3x - 1}{x}}$

$\displaystyle = \frac{3x + 1}{3x - 1}$

$\displaystyle = \frac{3x - 1 + 2}{3x - 1}$

$\displaystyle = 1 + \frac{2}{3x - 1}$.

Pick whichever form you think is "simplest".

5. Thanks.

Looks like on the LaTex in LyX that would take a display fraction rather than a standard fraction.