Dunno where to start!

[SilverSprite]

Could anybody maybe just give me a hint as to where to start for this question?

[bugzpodder]

let box=x^2-10x-45

[NotLKH]

Originally posted by bugzpodder
let box=x^2-10x-45

And if that fails, multiply every fraction by:

[bugzpodder]

lol. anywayz, if we just use y=x^2-10x-45

we have:

1/(y+16)+1/y=2/(y-24)

multiply BS by (y+16)y(y-24)

y^2-24y+y^2-8y-16*24=2(y^2+16y)

2*y^2-32y-16*24=2y^2+32y

-64y=16*24

-4y=24
y=-6

x^2-10x-45=-6
x^2-10x-39=0

(x-13)(x+3)=0

x=13 or -3

[krtxmrtz]

I think it's a little bit easier if you let

y = x² - 10x - 37

Then:

1 / (y + 8) + 1 / (y - 8) = 2 / (y - 32)

(y - 8 + y + 8) / (y² - 64) = 2 / (y - 32)

y / (y² - 64) = 1 / (y - 32)

y(y - 32) = y² - 64

y² - 32y = y² - 64

So, y=2 and:

x² - 10x - 37 = 2

x² - 10x - 39 = 0

And solving for x you get the same values, x = 13 and x = -3