# How to i manipulate this fraction

1. Feb 8, 2007

### seang

1. The problem statement, all variables and given/known data
I need to make this:

$$\frac{100K}{x^2 + (25 + \alpha)x + (\alpha 25 + 100K)}$$

look like this:

$$\frac{K}{x^2 + \beta x + (K)}$$

2. Relevant equations

Beta and K can be any combination of variables, as long as the top K and bottom K are equal. A scaling factor is allowed to come outside of the fraction if necessary.

3. The attempt at a solution

2. Feb 8, 2007

### HallsofIvy

Staff Emeritus
The "scaling factor" means that you can multiply either numerator or denominator to make them the same. Multiplying the denominator by something would change the "x2" term and, apparently, you don't want that. That means you must have something of the form
[tex]\frac{1}{C}\frac{100CK}{x^2+ (25+\alpha)x+ (25\alpha+ 100K)}[/itex]
It's pretty obvious what $\beta$ must be! Can you choose C and the new K so that the numerator and constant term in the denominator are the same? (You might want to initially call the new K something like K' to avoid confusion.)

3. Feb 9, 2007

### seang

alright, thank you.

But now, for the sake of argument, lets say I wasn't allowed to have a scaling factor outside of the fraction--what could I do then?