Turning a fraction into a quadratic

Larianne · #1 $Old$ December 2nd, 2008, 11:17 AM

Hi,

I'm trying to work out how a question was solved from an example in a book.

x(squared)
------------------- = 6.25
6 - 5x + x(squared)

goes to...

5.25x(squared) - 31.25x + 37.5 = 0

I don't understand how this was done.

any ideas?

nzmathman · #2 $Old$ December 2nd, 2008, 12:03 PM

They have cross multiplied to get the answer.

$\frac{x^2}{6 - 5x + x^2} = 6.25$

$\Rightarrow x^2 = 6.25(6 - 5x + x^2)$ (cross multiply)

$\Rightarrow x^2 = 37.5 - 31.25x + 6.25x^2$ (expanding)

$\Rightarrow 5.25x^2 - 31.25x + 37.5 = 0$ (collect terms on one side)