Simplifying question

Hello everyone,
This question is one of the basic simplifying questions which i couldn't understand.

Lets take this as an example:
1/x + 2/(x+1)

At some point we will get 3x+1/x(x+1)

My question is...in simplifying fractions why do we open brackets if they on top but we don't open them if they are in the denominator's place ?

Thanks

Quote:

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Originally Posted by Mathbeg

Hello everyone,
This question is one of the basic simplifying questions which i couldn't understand.

Lets take this as an example:
1/x + 2/(x+1)

At some point we will get 3x+1/x(x+1)

My question is...in simplifying fractions why do we open brackets if they on top but we don't open them if they are in the denominator's place ?

Thanks

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Hi Mathbeg,

Of course you could open the brackets and write the answer if you like. There is nothing wrong with it.

Quote:

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Originally Posted by Sudharaka

Hi Mathbeg,

Of course you could open the brackets and write the answer if you like. There is nothing wrong with it.

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Oh, my teacher told me it would be wrong.
maybe he meant wrong for GCSE only.

Quote:

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Originally Posted by Mathbeg

Oh, my teacher told me it would be wrong.
maybe he meant wrong for GCSE only.

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He was probably referring to the markscheme. Generally it's better to have things factored with fractions for GCSE exams. It's good practice for things like series, integration, proofs, inequalities and so forth later on when having factored numerators/denominators can make life very simple.

You need to get the denominator the same in each fraction before you can add. So, 1/x becomes 1(x+1)/x(x+1), and 2/(x+1) becomes 2(x)/x(x+1). At this point you can add the fractions being that the denominator in each is the same. So, what is 1(x+1) + 2(x)?

Quote:

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Originally Posted by Mathbeg

3x+1/x(x+1)

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I don't understand your question (what's opening a bracket?!) but
above should be: (3x + 1) / (x(x + 1))

9 + 6/3 = 9 + 2 = 11
(9 + 6)/3 = 15/3 = 5

1/x + 2/(x+1)
1(x+1) + 2 (x) why does this become 3x + 1 but the denominator stays x(x+1) instead of X^2 + X
I mean the numerator while not have brackets but the deno will

Quote:

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Originally Posted by Mathbeg

1(x+1) + 2 (x) why does this become 3x + 1

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1(x+1) + 2 (x) = x + 1 + 2x = 3x + 1

Looks like my question is confusing. :D

What i mean is: The numerator 1(x+1) + 2(x) why dont we keep it as it is as we did in the denominator ? the deno will be x(x+1) at the end, why not write x^2 + x as we did for the 1(x+1)..... in the numerator ?

Quote:

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Originally Posted by Mathbeg

....why not write x^2 + x as we did for the 1(x+1).....

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You could, but then it would be considered "not fully factored"; depends on original
problem statement ; 3x + 1 cannot be factored further, x^2 + x can.