first
solve for x
1/x-1 + 1/x =5
Hey cobber, please consider how you post these problems. For starters pls post 1 problem per thread and show your working to this point. Better we help you learn rather than do the problems for you.
My other concern is the lack of brackets. Why? Well which is your problem?
$\displaystyle \frac{1}{(x-1)} + \frac{1}{x} =5$
or
$\displaystyle \frac{1}{x}-1 + \frac{1}{x} =5$
I'm guessing the first one, but how can I be sure?
First things first, clear up some domain issues by saying $\displaystyle x \in \mathbb{R} \: , \: x \neq 0\,,\,1$
$\displaystyle
\frac{1}{(x-1)} + \frac{1}{x} =5
$
Take $\displaystyle \frac{1}{x}$ from both sides and rewrite $\displaystyle 5$ as $\displaystyle \frac{5x}{x}$ (this is allowed because $\displaystyle x \neq 0$)
$\displaystyle \frac{1}{x-1} = \frac{5x-1}{x}$
Cross multiply: $\displaystyle x = (5x-1)(x-1)$
Expand, simplify and solve the quadratic
Spoiler: