# Algebra simplifying

1. Apr 17, 2006

### jamie_23

I am in grade 11 mathematics...i got this as a Thinking & Problem Solving Q..can someone simplify this, step by step?

4 - 1/x
---------
4 + 1/x

THANKS!

2. Apr 17, 2006

### Integral

Staff Emeritus
You need to show us some of your work or thoughts on the problem.

Here's a hint. Clear the fractions first.

3. Apr 17, 2006

### jamie_23

ok..the way i thought was taking the negative reciprocal of the denominator..
making it (4-1/x)(4-1/x)
---------------
(4+1/x)(4-1/x)
=16-8 1/x+1/x^2
----------------
16-1/x^2

does that work?
I havent been taught how the clear the fractions.

4. Apr 17, 2006

### Integral

Staff Emeritus
Sure you have... Just think about it for a bit. What would you multiply top and bottom by?

5. Apr 18, 2006

### Cummings

Simplifying should never change the outcome of an equation. You can therefore check if your simplification is correct by letting x equal any number. The original and simplified equations will produce the same answer if the simplification is correct.

So, let x=2
Your first equation gives (4 - 1/2) / (4 + 1/2) = .77778
Your simplified equation gives (16 - 8/2 + 1/4) / (16 - 1/4) = .77778

So your simplification is correct however it is probably not a "simplification". It looks more complex. What Integral is saying is that you can get rid of a fraction by multiplying it (and all other parts of the equaion by the denomonator of the fraction. This is particularly usefull if you have the same problem in multiple parts fo the equation.

For example, (1 + 1/x) / (2 + 3/x) can be simplified by multiplying both the top and bottom lines by x (the denomonator of the fraction).

You then get (x + 1) / (2x + 3) - much simpler form than the original.
You can then multiply by the reciprical if you wish (gives you (-2x^2 + x + 3) / (-4x^2 + 9) ) but it is not as simple is it?

For the same reason as multiplying by the reciprical, multiplying both parts by the denomonator does not change the outcome of the equation because x/x = 1

6. Apr 22, 2006

### kuahji

If I understand this correctly, (4-1/x)/(4+1/x)

I'm not going to asnwer the question for you. But lets look at something simplier. (1/2)/(1/8) to make things simple multiply the two together like this (1/2) * (8/1) = (8/2) or 4. Just flip the bottom term upside (take the reciprocal) & multiply. Hope that helps.

7. Apr 28, 2006

### konartist

first, $$(4-1/x)/(4+1/x)$$ common denominators maybe?
$$(4/x-1/x)/(4/x+1x)$$
than
$$[(4x-1)/x]/[(4x+1/x)]$$
Multiply by the recpricoal of the denominator now.... Can you see?

You should see that some things will cancel.