# hard fraction

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• Nov 12th 2010, 05:59 AM
andyboy179
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!
• Nov 12th 2010, 06:06 AM
Ackbeet
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?
• Nov 12th 2010, 06:14 AM
andyboy179
oh sorry, im not too good with posting with all the codes!

this is the question:
Attachment 19677
• Nov 12th 2010, 06:16 AM
Ackbeet
Ok, let me write up your problem. Solve

\$\displaystyle \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?
• Nov 12th 2010, 06:20 AM
andyboy179
im not too sure how i would find that. would i be 1
• Nov 12th 2010, 06:22 AM
Ackbeet
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?
• Nov 12th 2010, 06:26 AM
andyboy179
im still not sure. would x+2? or 2?
• Nov 12th 2010, 06:27 AM
Ackbeet
What's the least common multiple of 2 and 3?
• Nov 12th 2010, 06:29 AM
andyboy179
6
• Nov 12th 2010, 06:30 AM
Ackbeet
So what's the LCM of 4 and 6?
• Nov 12th 2010, 06:32 AM
andyboy179
12, one question, i don't understand why we need to find the LCM?
• Nov 12th 2010, 06:35 AM
Ackbeet
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.)
• Nov 12th 2010, 06:37 AM
andyboy179
oh okay! i know the LCM between 2 and 2 is 2 but i get confused when the x comes in!
• Nov 12th 2010, 06:42 AM
Ackbeet
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?
• Nov 12th 2010, 06:44 AM
andyboy179
would it be 2x+2?
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