Factorize the polynomials in both numerator and denomiantor.
Cancel out common factors if any.
If the denominator and the numerator have no common factors except 1, then that is said to be the simplest form of the given rational expression.

<h3>Calculation:</h3>

The given rational equation is

$\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}$

Factorizing the expression in the numerator:

y² - 12y + 27 = y² - 9y - 3y + 27

⇒ y(y - 9) - 3(y - 9)

⇒ (y - 3)(y - 9)

Factorizing the expression in the denominator:

y² - 6y - 27 = y² - 9y + 3y - 27

⇒ y(y - 9) + 3(y - 9)

⇒ (y + 3)(y - 9)

Since they have (y - 9) as the common factor, we can simplify,

$\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}=\frac{(y-3)(y-9)}{(y+3)(y-9)}$

⇒ (y - 3)/(y + 3) where y ≠ -3(denomiantor)

Here there are no more common factors except 1; this is the simplest form of the given rational expression.

Learn more about simplifying rational expressions here:

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3 0

1 year ago

vampirchik [111]

Since 25% is 1/4 of 100%, then you do 8/4 and you get 2 and then you do 2 + 8 = 10.

7 0

3 years ago