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Help solving a hard quadratic equation.

It's not a normal one...

4 over x -2 + 6 over x + 2 = 1

and before someone asks, I don't just want to copy someone's answer. I have no idea how to start...can you maybe do a step-by-step method so I can work out some of the other questions myself and then post.

I'll try to do it though.

What I think:

Cross multiply? So 4(x+2) and 6(x-2)

4x+8 + 6x-12 = 1
so 10x^2 - 4 = 1
10x^2 - 4 - 1 = 0
10x^2 - 3 = 0
x = square root of 10 - 3

I know I'm probably wrong haha

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Reply 1
Avatar for TLK
TLK
8
Original post by ToLiveInADream
It's not a normal one...

4 over x -2 + 6 over x + 2 = 1

and before someone asks, I don't just want to copy someone's answer. I have no idea how to start...can you maybe do a step-by-step method so I can work out some of the other questions myself and then post.

I'll try to do it though.

What I think:

Cross multiply? So 4(x+2) and 6(x-2)

4x+8 + 6x-12 = 1
so 10x^2 - 4 = 1
10x^2 - 4 - 1 = 0
10x^2 - 3 = 0
x = square root of 10 - 3

I know I'm probably wrong haha


What about the (x+2)(x-2) on the RHS?
Reply 2
Avatar for Zeegie
Zeegie
16
what exactly is over what?

is it [4/(x-2+6)] / (x+2) = 1 ?

Is that what you mean?
Original post by Zeegie
what exactly is over what?

is it [4/(x-2+6)] / (x+2) = 1 ?

Is that what you mean?


Sorry, it isn't clear? :frown: 4/x-2 + 6/x+2 = 1
Original post by Zeegie
AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH :biggrin:

yep so cross multiply so you get 8x+8+6x-12=1

then just solve for x :smile:


wait, where did you get the 8x from?
Reply 5
Avatar for Cerdic
Cerdic
18
Original post by ToLiveInADream
Sorry, it isn't clear? :frown: 4/x-2 + 6/x+2 = 1


First times everything by the bottom of the fraction so

4/(x+4) = x+2

I also simplified x-2+6 to x+4. Can you do it from there? It might seem a little more obvious now
Original post by TLK
What about the (x+2)(x-2) on the RHS?


what do you mean?
Original post by ToLiveInADream


Cross multiply? So 4(x+2) and 6(x-2)

4x+8 + 6x-12 = 1
so 10x^2 - 4 = 1
10x^2 - 4 - 1 = 0
10x^2 - 3 = 0
x = square root of 10 - 3

I know I'm probably wrong haha


Not so much cross multiply, but rather multiply through by (x+2) and by (x-2)

There are some serious misconceptions here as well.

4x + 6x is 10x, not 10x^2

-4 -1 is -5, not -3.

I think you need to brush up on algebraic manipulation.
Reply 8
Avatar for bo536
bo536
2
4/(x-2) + 6/(x+2) = 1

4(x+2) + 6(x-2) = (x-2)(x+2) [Cross multiplication]

4x + 8 + 6x - 12 = x^2 - 4 [Expand brackets]

x^2 - 4 - 4x - 8 - 6x + 12 = 0 [LHS]

x^2 - 10x + 0 = 0 [Collect like terms]

x(x - 10) = 0, so x = 0 or x = 10 [Factorise] (either x or (x-10) must be 0 to multiply to give 0)

Or if you don't understand that last step, plug the quadratic into the quadratic equation, you'll get the same answer.
Reply 9
Avatar for TLK
TLK
8
Original post by ToLiveInADream
what do you mean?


When you cross multiply you are multiplying the 1 by (x+2) and then (x-2) or either way around. So you end up with (x+2)(x-2) on the right hand side.
I'm even more confused now...two contrasting answers.

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Sigh. I've just gotten back into maths after a year of something completely different and don't understand anything. Second point was a typo, but thanks for correcting the me for the other.

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Waah. Isn't this c3 stuff.

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Thanks :smile:

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Reply 14
Avatar for bo536
bo536
2
My answer is right, you can test it by trying 0 and 10 in the original equation. Also this is C1 level, for what it's worth
I think you need to use substitution.

E.g. X^-1 = y
X^-2 = y^2

Then solve. Then substitute back to find the x values. :smile:
Wait... I may have misunderstood what you mean by 'over'!

Feel free to ignore me if so, it's just not entirely clear what you mean. :s sorry
Original post by QuantumSuicide
Waah. Isn't this c3 stuff.

Posted from TSR Mobile


GCSE
C3 chapter 1 is pretty similar.

Posted from TSR Mobile
OP, all you have to do is get a common factor and cancel/factorise and continue to solve for X.

Posted from TSR Mobile

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