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

[tehmatriks]

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

 

[spamiam]

Throw some parentheses in there:

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

and you should get the answer in the back of the book.

 

[tehmatriks]

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

 

[Mark44]

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.

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.

and i did it another way where i got 1 1/9
but i can't seem to get 2 3/10

 

[tehmatriks]

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.

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

no wait, scratch that, i don't understand anything, forget i asked

 

[Mark44]

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
$$\frac{2}{x} + 2 + \frac{3}{2x} + 1$$

or even as
$$\frac{2}{x} + 2 + \frac{3}{2}x + 1$$


which is not at all what you intended.

nice job, thanks

You're welcome!

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) = 2/(5/2)

and i apologize for my idiocy thus far

The goal is to get you to learn from your mistakes.

 

[tehmatriks]

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 beggining, 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