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Algebraic Fraction

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I got the answer to be -7 over -3 is that correct

thanks.

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Reply 1
No, that's not right. Post your working.
I believe the answer is: 2x27x(2x3)\frac{2x^2 - 7}{x (2x - 3)}

Post your working so we can see what the problem is.
Reply 3
2x(x)-7/x(2x-3)x(2x-3)
2x^2-7/2x^2-3
2x^2 cancels out so you're left with -7/-3
Reply 4
Original post by AtomSmasher
I believe the answer is: 2x27x(2x3)\frac{2x^2 - 7}{x (2x - 3)}

Post your working so we can see what the problem is.


Oh now I see where I have gone wrong.

I shouldn't have multiplied out the denominator.
Reply 5
Original post by zed963

2x^2-7/2x^2-3
2x^2 cancels out so you're left with -7/-3


You cannot cancel terms in a fraction, only factors. 2x^2 is not a factor of the numerator or the denominator.

Please let me know if you're not confident with this and I could explain further or give you some questions.
(edited 11 years ago)
Original post by zed963
2x(x)-7/x(2x-3)x(2x-3)
2x^2-7/2x^2-3
2x^2 cancels out so you're left with -7/-3


I the denominator is meant to be 2x23x2x^2 - 3x.
Remember, you can only cancel out common factors and since 2x22x^2 isn't a factor you can't cancel it out.
Reply 7
Original post by AtomSmasher
I the denominator is meant to be 2x23x2x^2 - 3x.
Remember, you can only cancel out common factors and since 2x22x^2 isn't a factor you can't cancel it out.


But if I expand the top I get 2x^2 and in the the denominator it is the same so why can't I cancel them out.
Reply 8
Original post by notnek
You cannot cancel terms in a fraction, only factors. 2x^2 is not a factor of the numerator or the denominator.

Please let me know if you're not confident with this and I could explain further or give you some questions.


Sure give me some questions.
This is a very common misconception and it is terribly wrong. I suggest you take notnek up on his offer if you don't understand why your attempt doesn't work.
Reply 10
Original post by zed963
Sure give me some questions.


Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

e.g. 3xy+2x

The two terms here are 3xy and 2x.

A factor is something which is part of a product.

e.g. 3xy + 2x

In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

e.g. x(x+2)x\displaystyle \frac{x(x+2)}{x}

x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

x+21=x+2\displaystyle \frac{x+2}{1}=x+2

Next example:

2xy+32xy(3z)\displaystyle \frac{2xy+3}{2xy(3z)}

There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

Now try simplifying these fractions:

a) 3(x+5)(x+2)2(x+2)\displaystyle \frac{3(x+5)(x+2)}{2(x+2)}

b) 3x+2z2z\displaystyle \frac{3x+2z}{2z}

c) 3(x+3)+5(x+3)(x+2)\displaystyle \frac{3(x+3)+5}{(x+3)(x+2)}

d) 3(x+2)+2(x+2)(x+2)(x+1)\displaystyle \frac{3(x+2)+2(x+2)}{(x+2)(x+1)}

For d), try simplifying the numerator.
(edited 11 years ago)
Original post by zed963
But if I expand the top I get 2x^2 and in the the denominator it is the same so why can't I cancel them out.


You can only cancel them out if they are factors, i.e., when multiplied by something else (not added or subtracted from) it makes the expression. You know all about factorising right?

I'll just do a very simple example, it always helps: You can factorise 4x6x\frac{4x}{6x} to 2×2x3×2x\frac{2 \times 2x}{3 \times 2x}. Since 2x is a common factor you can cancel it out, getting 23\frac{2}{3}. However, you can express the same fraction as 2x+2x4x+2x\frac{2x + 2x}{4x + 2x}, but since these are not factors, you can't cancel them out. If you tried cancelling them, you'd end up with 2x4x\frac{2x}{4x}, which obviously isn't the same.

Sorry if this seems like a kind of childish explanation, I'm sure you know what I mean though?
(edited 11 years ago)
Reply 12
Original post by notnek
Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

e.g. 3xy+2x

The two terms here are 3xy and 2x.

A factor is something which is part of a product.

e.g. 3xy + 2x

In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

e.g. x(x+2)x\displaystyle \frac{x(x+2)}{x}

x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

x+21=x+2\displaystyle \frac{x+2}{1}=x+2

Next example:

2xy+32xy(3z)\displaystyle \frac{2xy+3}{2xy(3z)}

There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

Now try simplifying these questions:


Okay
Reply 13
Original post by AtomSmasher
You can only cancel them out if they are factors, i.e., when multiplied by something else (not added or subtracted from) it makes the expression. You know all about factorising right?

I'll just do a very simple example, it always helps: You can factorise 4x6x\frac{4x}{6x} to 2×2x3×2x\frac{2 \times 2x}{3 \times 2x}. Since 2x is a common factor you can cancel it out, getting 23\frac{2}{3}. However, you can express the same fraction as 2x+2x4x+2x\frac{2x + 2x}{4x + 2x}, but since these are not factors, you can't cancel them out. If you tried cancelling them, you'd end up with 2x4x\frac{2x}{4x}, which obviously isn't the same.

Sorry if this seems like a kind of childish explanation, I'm sure you know what I mean though?


Yeah .
Reply 14
Original post by notnek
Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

e.g. 3xy+2x

The two terms here are 3xy and 2x.

A factor is something which is part of a product.

e.g. 3xy + 2x

In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

e.g. x(x+2)x\displaystyle \frac{x(x+2)}{x}

x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

x+21=x+2\displaystyle \frac{x+2}{1}=x+2

Next example:

2xy+32xy(3z)\displaystyle \frac{2xy+3}{2xy(3z)}

There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

Now try simplifying these fractions:

a) 3(x+5)(x+2)2(x+2)\displaystyle \frac{3(x+5)(x+2)}{2(x+2)}

b) 3x+2z2z\displaystyle \frac{3x+2z}{2z}

c) 3(x+3)+5(x+3)(x+2)\displaystyle \frac{3(x+3)+5}{(x+3)(x+2)}

d) 3(x+2)+2(x+2)(x+2)(x+1)\displaystyle \frac{3(x+2)+2(x+2)}{(x+2)(x+1)}

For d), try factorising the numerator.


For a) 3x+15/2
b) 3x
(edited 11 years ago)
Reply 15
Original post by zed963
For a) 3x+15/2(x+2)


No, try again.
Reply 16
Original post by raheem94
No, try again.


3x+15/2
Reply 17
Original post by zed963
3x+15/2


:yep:
:congrats:
Reply 18
Original post by raheem94
:yep:
:congrats:


For b) 3x
Reply 19
Original post by zed963
3x+15/2


Remember you should write it as (3x+15)/2, otherwise it is ambiguous.

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