Question

Y^2 - 12y + 27 / y^2 - 6y - 27 simply the rational equation.

Answer 1

The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.

How to simplify a rational expression?

A rational expression is in the p/q form. Where p and q are polynomial functions.

To simplify this rational equation,

• 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.

Calculation:

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:

brainly.com/question/1928496

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