# I need help solving these rational equations.

• Oct 27th 2009, 12:57 PM
Pre-Calc
I need help solving these rational equations.
first
solve for x
1/x-1 + 1/x =5
• Oct 27th 2009, 01:03 PM
pickslides
Quote:

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?

$\frac{1}{(x-1)} + \frac{1}{x} =5$

or

$\frac{1}{x}-1 + \frac{1}{x} =5$

I'm guessing the first one, but how can I be sure?
• Oct 27th 2009, 01:09 PM
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.
• Oct 27th 2009, 01:21 PM
e^(i*pi)
Quote:

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 $x \in \mathbb{R} \: , \: x \neq 0\,,\,1$

$
\frac{1}{(x-1)} + \frac{1}{x} =5
$

Take $\frac{1}{x}$ from both sides and rewrite $5$ as $\frac{5x}{x}$ (this is allowed because $x \neq 0$)

$\frac{1}{x-1} = \frac{5x-1}{x}$

Cross multiply: $x = (5x-1)(x-1)$

Expand, simplify and solve the quadratic :)

Spoiler:
$5x^2-6x+1 = x \: \rightarrow \: 5x^2-7x+1 = 0$

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

$= \frac{7 \pm \sqrt{(-7)^2-(4)(5)(1)}}{(2)(5)} = \frac{7 \pm \sqrt{29}}{10}$
• Oct 27th 2009, 01:27 PM
Pre-Calc
ty.