Math Is Fun Forum

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Constant / Fraction

What is the common method to work out a fraction with three stages?

I have 6/x and I've worked out x=-3/2 :
6/(-3/2)

I may have the wrong value for x, but I'd still like to know a good method for doing this

Thanks in advance.

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Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Constant / Fraction

Well,

Now, if you remember back to basic division, to divide you must reciprocate the denominator and multiply it to the numerator:

Last edited by Toast (2007-01-28 23:03:33)

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Constant / Fraction

One way to think about it is with fraction multiplication - when you divide by a/b, it's equivalent to multiplying by b/a (i.e. the inverse of a/b).

So, your problem poses how to find:

which is the same as doing:

All clear?

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RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Re: Constant / Fraction

Okay, that's brilliant and I understand how to do it! Thanks.

Could you have a look at my working out here? I'm not sure where I have gone wrong:

Find the points where the given line meets the given curve:

2x - 5y + 17 = 0   meets     xy = 6

Firstly I get y on its own:

5y = 2x + 17                       y = 6/x

y = 2/5x + 17/5

Now I can place the two side by side:

2/5x + 17/5 = 6/x

Now I balance and collect all the terms:

2/5x^2 + 17/5x = 6

2x^2 + 17x = 30

2x^2 + 17x - 30 = 0

Now I find two numbers whose sum is 17 and product is 2*-30 (or -60).  These two numbers are +20 and -3, I re-write the quadratic:

2x^2 - 20x + 3x - 30 = 0

Now I take out the common factor of the first two numbers, then the second two numbers making sure that both sets of brackets are the same:

2x^2 - 20x         + 3x - 30        = 0
2x(x-10)             + 3(x-10)       = 0

This leaves me with:
(2x+3)(x-10)

So x=10 or x=-3/2

I substitute these values into y=6/x to give me

y=6/10   and     y=6/(-3/2)=-4

So the answer should be that the line intersects the curve at (10, 6/10) and (-3/2, -4).  My book gives the answers with the signs reversed!:

(3/2, 4) and (-10, -3/5)

Whose signs are backwards?

Edit:

These two numbers are +20 and -3, I re-write the quadratic:

2x^2 - 20x + 3x - 30 = 0

My signs are wrong Thanks again!

Last edited by rickyoswaldiow (2007-01-28 23:33:06)

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Aloha Nui means Goodbye.