Algebraic Fraction

Original post by zed963

For b) 3x

No, try again.

Notice that there are 2 variable, 'x' and 'z'.

For c) 8/(x+2)

Original post by raheem94

No, try again.

Notice that there are 2 variable, 'x' and 'z'.

(5xz)/2z

Reply 23

Original post by zed963

For c) 8/(x+2)

, try again.

Reply 24

AtomSmasher

Original post by zed963

For b) 3x

No, try again. Remember you can only cancel out factors.

Reply 25

Original post by zed963

b) 3x

Look at the whole numerator. It contains 2 terms (3x and 2z) but only one factor (3x+2z). But this factor is only a factor of the numerator so you cannot cancel it. Another example:

\displaystyle \frac{(3x)(2z)}{3x}

Here, the whole numerator contains 1 term ( (3x)(2z) ) and there are two factors in that term (3x and 2z). Since there is only one term, these factors are factors of the whole numerator. The denominator also contains the factor 3x so you can cancel it. One more:

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

The whole numerator contains two terms, (3x)(2z) and 5. The whole numerator contains only one factor: ((3x)(2z)+5). 3x is a factor of the denominator but not the numerator so you cannot cancel it. Remember, ((3x)(2z)+5) is the only factor of the numerator.

Does this make sense?

(edited 11 years ago)

Reply 26

Original post by zed963

(5xz)/2z

Question 'b' can't be simplified further.

Reply 27

mrdoovde1

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

\frac{4x}{6x}

\frac{2 \times 2x}{3 \times 2x}

. Since 2x is a common factor you can cancel it out, getting

\frac{2}{3}

. However, you can express the same fraction as

\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

\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?

Sorry don't mean to hijack this thread but what about this as an example

\frac{7x^6+9}{7x^4+2}

Does that equal to

\frac{7x^2+9}{2}

Reply 28

Original post by mrdoovde1

Sorry don't mean to hijack this thread but what about this as an example

\frac{7x^6+9}{7x^4+2}

Does that equal to

\frac{7x^2+9}{2}

No.

You are cancelling

7x^4

, since you're assuming that it's a factor of the numerator and the denominator. But it isn't.

Look at the numerator. If

7x^4

was a factor of it then it must be multiplied by something else to make up the whole of the numerator. It's not though.

e.g. look at this expression:

7\times 4 + 9

. Would you say that 4 is a factor of the whole of this expression? No. It's only a factor of the first term,

7\times 4

.

You can only cancel something in an algebraic fraction if it is a factor of the whole numerator and the whole denominator.

(edited 11 years ago)

Reply 29

Original post by raheem94

, try again.

What am I doing wrong can you give me a clue.

Reply 30

Original post by raheem94

Question 'b' can't be simplified further.

So whats the answer.

Reply 31

Original post by zed963

What am I doing wrong can you give me a clue.

Remember, some expressions can't be simplified.

Reply 32

Original post by zed963

So whats the answer.

The question is the answer, it can't be simplified so leave it as it is. Notnek wanted to test your understanding hence he put in some questions that can't be simplified.

Reply 33

Original post by zed963

So whats the answer.

Some of the questions that I included cannot be simplified. I put them in to show you the times when you cannot cancel in an algebraic fraction.

The answer would be the same as the question.

Reply 34

Original post by raheem94

Remember, some expressions can't be simplified.

I though question c could be simplified because it has a common factor of x+2

Reply 35

Original post by zed963

I though question c could be simplified because it has a common factor of x+2

How is (x+2) a common factor?

Do you really think 'c' can't be simplified further?

Reply 36

AtomSmasher

Original post by zed963

What am I doing wrong can you give me a clue.

For the time being (until you get a good grasp of it) try factorising the numerator and denominator as far as they will go, then just cancel out any factors (multiples) that occur on both the top and the bottom.

Reply 37

Original post by raheem94

How is (x+2) a common factor?

Do you really think 'c' can't be simplified further?

I meant x+3

so it becomes 8/x+2

Reply 38

Original post by zed963

I meant x+3

so it becomes 8/x+2

(x+3) is a factor of the denominator but not of the numerator.

Reply 39