# Thread: I need help solving these rational equations.

1. ## I need help solving these rational equations.

first
solve for x
1/x-1 + 1/x =5

2. Originally Posted by Pre-Calc
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?

3. the first one is my problem im new to this forum so i didn't no how to put it that way sorry.

4. Originally Posted by Pre-Calc
the first one is my problem im new to this forum so i didn't no how to put it that way sorry.
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:
$\displaystyle 5x^2-6x+1 = x \: \rightarrow \: 5x^2-7x+1 = 0$

$\displaystyle x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$\displaystyle = \frac{7 \pm \sqrt{(-7)^2-(4)(5)(1)}}{(2)(5)} = \frac{7 \pm \sqrt{29}}{10}$

5. ty.