How Do You Solve 2/x+2 + 3/2x+1 for x=1/2?

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Homework Help Overview

The discussion revolves around evaluating the expression 2/x + 2 + 3/2x + 1 at x = 1/2, with the original poster referencing a solution from the back of a textbook that states the answer is 2 3/10.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the correct interpretation of the expression, with emphasis on the importance of parentheses. There are attempts to evaluate the expression using different methods, leading to confusion about the correct setup and calculations.

Discussion Status

Some participants have provided guidance on the use of parentheses and the correct interpretation of the expression. There is acknowledgment of misunderstandings and attempts to clarify the steps involved in reaching the solution. Multiple interpretations of the expression are being explored, but no consensus has been reached on the correct method.

Contextual Notes

Participants have noted the potential for misinterpretation due to the lack of parentheses in the original expression, which may have led to different calculations and results. There is also mention of frustration and confusion stemming from the complexity of the problem.

tehmatriks
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Question is:
Evaluate 2/x+2 + 3/2x+1 when x= ½

back of the book says 2 and three tens i.e 2 3/10
 
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Throw some parentheses in there:

2/(x+2) + 3/(2x+1)

and you should get the answer in the back of the book.
 
i know, i checked the back of the book and it says the answer is 2 3/10

this is how I am doing it:
2/x+2 + 3/2x+1
=> 2/½+2 + 3/2(½)+1
=> 2/2½ + 3/2, get LCM of 2½ and 2, which is 10
=> 10(2)/2½ + 10(3)/2
=> 4(2) + 5(3)
=> 8 + 15 = 23

and i did it another way where i got 1 1/9
but i can't seem to get 2 3/10
 
tehmatriks said:
i know, i checked the back of the book and it says the answer is 2 3/10
Did you not understand spamiam's comment about parentheses? You seem to have glossed right over it.
tehmatriks said:
this is how I am doing it:
2/x+2 + 3/2x+1
=> 2/½+2 + 3/2(½)+1
=> 2/2½ + 3/2, get LCM of 2½ and 2, which is 10
=> 10(2)/2½ + 10(3)/2
=> 4(2) + 5(3)
=> 8 + 15 = 23
1.Use parentheses when a numerator or denominator (or both) have two or more terms.
2. Do not use => (implies) when you mean = (equals).

If x = 1/2, then 2/(x + 2) + 3/(2x + 1) = 2/(5/2) + 3/2 = 2 * 2/5 + 3/2 = 4/5 + 3/2

Now, the LCM of 5 and 2 is 10, so multiply the first fraction by 2/2 and the second by 5/5. After you do this, you will be able to combine the two fractions.

The answer in the book is correct.

tehmatriks said:
and i did it another way where i got 1 1/9
but i can't seem to get 2 3/10
 
Mark44 said:
Did you not understand spamiam's comment about parentheses? You seem to have glossed right over it.
nah, i didn't, i had no idea you had to put it in parentheses when you had more than one term in either the numerator or the denominator.

Mark44 said:
1.Use parentheses when a numerator or denominator (or both) have two or more terms.
2. Do not use => (implies) when you mean = (equals).

If x = 1/2, then 2/(x + 2) + 3/(2x + 1) = 2/(5/2) + 3/2 = 2 * 2/5 + 3/2 = 4/5 + 3/2

Now, the LCM of 5 and 2 is 10, so multiply the first fraction by 2/2 and the second by 5/5. After you do this, you will be able to combine the two fractions.

The answer in the book is correct.
nice job, thanks
only bit i don't understand is why and how 2/(½+1) became 2/(5/2)

and i apologize for my idiocy thus far :smile:

no wait, scratch that, i don't understand anything, forget i asked
 
Last edited:
tehmatriks said:
nah, i didn't, i had no idea you had to put it in parentheses when you had more than one term in either the numerator or the denominator.
The problem is that when you write 2/x + 2 + 3/2x + 1, knowledgeable people will probably interpret this as
[tex]\frac{2}{x} + 2 + \frac{3}{2x} + 1[/tex]

or even as
[tex]\frac{2}{x} + 2 + \frac{3}{2}x + 1[/tex]


which is not at all what you intended.
tehmatriks said:
nice job, thanks
You're welcome!
tehmatriks said:
only bit i don't understand is why and how 2/(½+1) became 2/(5/2)
It didn't, but 2/(1/2 + 2[/color]) = 2/(5/2)
tehmatriks said:
and i apologize for my idiocy thus far :smile:
The goal is to get you to learn from your mistakes.
 
ok I am back, thanks for the help mark, i realized what i was doing wrong, i took it too far, i got the answer pretty much right at the beginning, except it all went downhill when i used the LCM

anyway, preciate the help fellas, I've been trying to figure this out for 6+ hrs and was getting alittle depressed, happy now tho, peace
 

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