# Math Help - hard fraction

1. ## hard fraction

hi, this is my question:
solve
x-1/2 - 4/x+2=1?

so far i have got (x-1)(x+2)/ 2x+4 - 8/ 2x+4=1

i don't know what i would do from here so could someone please explain how to do this please?

not sure but would i times the 2 brackets to make, x^2 + x -2?

Thanks!

2. I think you should be more careful with parentheses. Do you mean x-(1/2) or, as I suspect, (x-1)/2? There are too many ambiguities here for me to parse what you mean. Can you add some parentheses, please?

3. oh sorry, im not too good with posting with all the codes!

this is the question:

4. Ok, let me write up your problem. Solve

$\dfrac{x-1}{2}-\dfrac{4}{x+2}=1$

for x. Is that correct? If so, the first thing you're going to need to do is get a common denominator on the LHS. What is the common denominator?

5. im not too sure how i would find that. would i be 1

6. It's the "least common multiple" of the denominators. But you have to view things like x+2 as a single factor. So what do you think?

7. im still not sure. would x+2? or 2?

8. What's the least common multiple of 2 and 3?

9. 6

10. So what's the LCM of 4 and 6?

11. 12, one question, i don't understand why we need to find the LCM?

12. Correct. I'm trying to help you with an analogy. Finding the common denominator is THE SAME as finding the least common multiple of the denominators. And it works the same way for factors like x+2 as it does for numbers. So, what is the common denominator for your two fractions? (Your answer in post # 7 is incorrect, but you're on the right track.)

13. oh okay! i know the LCM between 2 and 2 is 2 but i get confused when the x comes in!

14. You're not the only one who gets confused by this, trust me. Think of x+2 as (x+2). That is, when you compute the LCM of (2) and (3), you viewed (2) as a "factor" and (3) as a "factor". With these two denominators, you have to view (2) as a factor and (x+2) as a factor. Does that help? If so, what do you think is the common denominator?

15. would it be 2x+2?

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