# How do you solve 2/(x+1) + 5/(x-2)=-2?

Aug 6, 2018

$x = - 3 \mathmr{and} x = \frac{1}{2}$

#### Explanation:

Here ,

$\frac{2}{x + 1} + \frac{5}{x - 2} = - 2$

Combine the fractions :

$\frac{2 \left(x - 2\right) + 5 \left(x + 1\right)}{\left(x - 2\right) \left(x + 1\right)} = \frac{- 2 \left(x + 1\right) \left(x - 2\right)}{\left(x + 1\right) \left(x - 2\right)}$

Simplifying we get

$2 \left(x - 2\right) + 5 \left(x + 1\right) = - 2 \left(x + 1\right) \left(x - 2\right)$

Using distributive property :

$2 x - 4 + 5 x + 5 = - 2 \left({x}^{2} - 2 x + x - 2\right)$

$\therefore 7 x + 1 = - 2 {x}^{2} + 2 x + 4$

$\therefore 2 {x}^{2} + 5 x - 3 = 0$

$\therefore 2 {x}^{2} + 6 x - x - 3 = 0$

$\therefore 2 x \left(x + 3\right) - 1 \left(x + 3\right) = 0$

$\therefore \left(x + 3\right) \left(2 x - 1\right) = 0$

$\therefore x + 3 = 0 \mathmr{and} 2 x - 1 = 0$

$\therefore x = - 3 \mathmr{and} x = \frac{1}{2}$
The text contains a mathematical question in the form of an equation to solve, and it provides a detailed step-by-step solution leading to the 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 2/(x+1) + 5/(x-2)=-2?

Aug 6, 2018

$x = - 3 \mathmr{and} x = \frac{1}{2}$

#### Explanation:

Here ,

$\frac{2}{x + 1} + \frac{5}{x - 2} = - 2$

Combine the fractions :

$\frac{2 \left(x - 2\right) + 5 \left(x + 1\right)}{\left(x - 2\right) \left(x + 1\right)} = \frac{- 2 \left(x + 1\right) \left(x - 2\right)}{\left(x + 1\right) \left(x - 2\right)}$

Simplifying we get

$2 \left(x - 2\right) + 5 \left(x + 1\right) = - 2 \left(x + 1\right) \left(x - 2\right)$

Using distributive property :

$2 x - 4 + 5 x + 5 = - 2 \left({x}^{2} - 2 x + x - 2\right)$

$\therefore 7 x + 1 = - 2 {x}^{2} + 2 x + 4$

$\therefore 2 {x}^{2} + 5 x - 3 = 0$

$\therefore 2 {x}^{2} + 6 x - x - 3 = 0$

$\therefore 2 x \left(x + 3\right) - 1 \left(x + 3\right) = 0$

$\therefore \left(x + 3\right) \left(2 x - 1\right) = 0$

$\therefore x + 3 = 0 \mathmr{and} 2 x - 1 = 0$

$\therefore x = - 3 \mathmr{and} x = \frac{1}{2}$
user
The text contains a mathematical question in the form of an equation to solve, and it provides a detailed step-by-step solution leading to the answers.

TYPE: SINGLE_QUESTION_WITH_ANSWER