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The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.
<h3>How to simplify a rational expression?</h3>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.
The given rational equation is
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,
⇒ (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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we are given
quadratic equation as
now, we can find b and c from
we can see that coefficient of x^2 is 1
so, we will have to make coefficient x^2 as 1
so, we divide both sides by 3
now, we can simplify it
now, we can compare it with
we get
so, we get order pair as
..............Answer