# How to i manipulate this fraction

## Homework Statement

I need to make this:

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

look like this:

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

## Homework 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.

## The Attempt at a Solution

HallsofIvy
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.)