Problem on solving a quadrtic equation

Topic:-quadratic equation

A quadratic equation is equation is a polynomial equation of the second degree. The general form is

where x represents a variable, and a, b, and c, represent constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.)
The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. Quadratic comes from quadratus, which is the Latin word for "square."
This math help gives a example as well.


Question:-

x2-12x+27       x+9
---------  *  -------
x2-81           3-x

Answer:-

Let's start with simplifying the quadratic expression

x2-12x+27

x2-3x-9x+27

x(x+3)-9(x-3)

(x-3)(x-9)

Let's substitute it back in the given equation


(x-3)(x-9)      x+9
---------  *  -------
x2-81          3-x



(x-3)(x-9)      x+9
----------  *  -------
(x+9)(x-9)      3-x


Cancel the similar terms on numerator with denominator

We get

 x-3
-------
 3-x

We can write 3-x as -(x-3)

So     x-3
   ------- = -1
   -(x-3)

So -1 is the answer.