Quadratics with equations!!!!:( HELP

shortys94

Hey
I am usually good at maths but as soon as i got to this chapter in school i am so confused, i cant get some of the sums, and am not sure if simplifying a fraction is the same as solving.

Could you help me with these two sums first of all and explain how to do it????

1 - 1 = 1

---

-- ----

---

x-1 x+1 4


3 - 1 = 1

---

---

---

x+2 x-1 10

Please help me, remember there quadtratics so i need to answers for x, i mainly just want someone to work it out and beside there workings tell me why they did certain things and so on....

Thanks:)

Yakuza

Hi,
Ah good old quadratic equations

The first one is fairly easy

 1  -  1   =  1
---   ---    ---
x-1   x+1     4

the trick here is to "cross multiply" the stuff on the left hand side of the equation
To do this, you multiply the numerator (top) part of the leftmost of the fractions by the denominator (bottom) of the rightmost of the fractions.

You then add the product of the top part of the right fraction and the bottom part of the left fraction.

The whole lot gets then divided by the product of both bottom parts.

Let me show you a numbered example:

 1  -  1   =  ?
---   ---   
3       6     

The cross multiplication of these two fractions would be

6(1) - 3(1)
------------
   (3)(6)

Which is the same as 3/18 (which simplifies to 1/6).

In the case of our example above, the cross product is:

1(x+1) - 1(x-1)   
-------------- 
  (x-1)  (x+1)     

Multiplying this out, (and watching for minus signs!!), this becomes:

x+1 -  x+1   
-------------- 
  x²-1    

which further reduces to 2/(x²-1)

So, the original equation is now:

 2   =  1
----   ---
x²-1    4

Multiplying this out, yields :

8 = x²-1

Or x² = 9, so x=3 (or -3).

And indeed, checking....1/(3-1) - (1/(3+1)) = 1/4!

The second question is a little more complex, but not much.

Starting with the original question:

 3  -  1   =  1
---   ---    ---
x+2   x-1    10

Cross multplying yields:

3(x-1) - 1(x+2) 
------   ------   
(x+2)   (x-1)   

Which reduces to:

2x -5 
-------
x²+x-2

And our orignal question is now:

2x -5      1
------- = ----
x²+x-2     10

Multiplying this out yields:
20x -50 = x²+x-2.

Expressing this as a quadratic (ax²+bx+c) yields:

x² - 19x + 48 =0


Using the trusty old equation

        b±√(b²-4ac)
  x = ------------------
             2a

And plugging in the values for a, b, c yields

x = (19±√(19²-4*1*48))/2

x = (19 ± 13) /2

or, x = 3 or 16.

I hope that helped

breadmonkey

fair play, you put quite a bit of effort into that post!

shortys94

thanks for that:)
sorry but it ended up i just made stupid mistakes and actually got answers right:)
i just got lcm of each and multiplies,