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# Algebraic Fraction Help.

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1. Hi, would somebody be able to demonstrate how these type of questions are done. I don't mean to be needy, but could you annotate so I can get a proper understanding.

Thanks!

Simplify

Simplify
2. You look for common factors

With ordinary numbers you know that

You know that you can cancel the 6 x because it is in the numerator and the denominator

In the same way

has (x+2) multiplying in both the numerator and denominator so it can be cancelled

3. First one, cancel out common factor of x + 5

Second one factorise the numerator(difference of two squares) and the denominator and then cancel out the common factor of x + 3
4. (Original post by TenOfThem)
You look for common factors

With ordinary numbers you know that

You know that you can cancel the 6 x because it is in the numerator and the denominator

In the same way

has (x+2) multiplying in both the numerator and denominator so it can be cancelled

(Original post by Mr M)
First one, cancel out common factor of x + 5

Second one factorise the numerator(difference of two squares) and the denominator and then cancel out the common factor of x + 3
For the first one, does that become
5. (Original post by TheMysteryMan)
For the first one, does that become
Apart from the fact that 2 goes into 6, yes
6. (Original post by TheMysteryMan)
For the first one, does that become
Yes, but it can be made even simpler. Expand the brackets and try to simplify further.
7. (Original post by CharlieBoardman)
Yes, but it can be made even simpler. Expand the brackets and try to simplify further.

3x+15 ?
8. (Original post by TheMysteryMan)

3x+15 ?
Correct
9. Remember to exclude values of x that make the denominator zero - from the domain:
first one: x =/= -5
second one: x =/= 0, -3 in your final answer!
10. (Original post by TheMysteryMan)

3x+15 ?
Yes but I would suggest dividing the 6 by 2 would be a better move.
11. (Original post by tomctutor)
Remember to exclude values of x that make the denominator zero - from the domain:
first one: x =/= -5
second one: x =/= 0, -3 in your final answer!
At this level, that is not necessary.
12. (Original post by tomctutor)
Remember to exclude values of x that make the denominator zero - from the domain:
first one: x =/= -5
second one: x =/= 0, -3 in your final answer!
You lost me
13. For the 2nd one, am I factorising top and bottom first?
14. (Original post by TheMysteryMan)
You lost me
don't worry ... he was answering a more complex question
15. (Original post by TheMysteryMan)
You lost me
Don't worry, you do not need to know that yet.
16. (Original post by TenOfThem)
don't worry ... he was answering a more complex question

(Original post by CharlieBoardman)
Don't worry, you do not need to know that yet.
Ok, would you be able to explain the 2nd one a little more to me, not sure where to start. Am I factorising out the top and bottom?
17. (Original post by TheMysteryMan)
Ok, would you be able to explain the 2nd one a little more to me, not sure where to start. Am I factorising out the top and bottom?
Yes, but try to look for the 'difference of two squares' somewhere. Once the numerator and denominator have been factorised correctly, they should have a term in common which you will be able to cancel.
18. I don't think i've been taught that, only the quadratic formula, factorising and graphs.
19. (Original post by TheMysteryMan)
I don't think i've been taught that, only the quadratic formula, factorising and graphs.
You've not been taught the difference of two squares?

x^2-4=x^2-2^2=(x+2)(x-2)

Hence difference of squares?
20. Is the answer -3?

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