# How do you solve x-4/x-1 = 12/3-x +1?

## solving rational equations

Jul 20, 2018

$x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$

#### Explanation:

$x - \frac{4}{x} - 1 = \frac{12}{3} - x + 1$ where $x \ne 0$

$x - \frac{4}{x} - 1 = 4 - x + 1$

$2 x - 6 = \frac{4}{x}$

$2 {x}^{2} - 6 x = 4$

$2 {x}^{2} - 6 x - 4 = 0$

${x}^{2} - 3 x - 2 = 0$

$x = \frac{3 \pm \sqrt{9 + 8}}{2}$
$x = \frac{3 \pm \sqrt{17}}{2}$
$x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
The text passage contains a mathematical question in the form of an equation to solve, and it provides a detailed step-by-step solution leading to the final answers.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# How do you solve x-4/x-1 = 12/3-x +1?

## solving rational equations

Jul 20, 2018

$x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$

#### Explanation:

$x - \frac{4}{x} - 1 = \frac{12}{3} - x + 1$ where $x \ne 0$

$x - \frac{4}{x} - 1 = 4 - x + 1$

$2 x - 6 = \frac{4}{x}$

$2 {x}^{2} - 6 x = 4$

$2 {x}^{2} - 6 x - 4 = 0$

${x}^{2} - 3 x - 2 = 0$

$x = \frac{3 \pm \sqrt{9 + 8}}{2}$
$x = \frac{3 \pm \sqrt{17}}{2}$
$x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
user
The text passage contains a mathematical question in the form of an equation to solve, and it provides a detailed step-by-step solution leading to the final answers.

TYPE: SINGLE_QUESTION_WITH_ANSWER