Question

Simplify the expression: y²-6y/y²+2y-24 . y-4/y²+12y+36 ÷ y²+y-42/y²

Answer 1

To simplify the expression, factor the numerator and denominator if possible, cancel common factors, and multiply and combine like terms.

Step-by-step explanation:

To simplify the expression:
y²-6y/y²+2y-24 . y-4/y²+12y+36 ÷ y²+y-42/y²

1. Factor numerator and denominator if possible
2. Cancel common factors
3. Multiply and combine like terms

Let's go step by step.

Step 1:
Factor the numerator and denominator if possible:

y²-6y/y²+2y-24 = y(y-6)/(y+6)(y-4)

y-4/y²+12y+36 can be factored as y-4/(y+6)²

y²+y-42/y² can be factored as (y-6)(y+7)/(y)(y)

Step 2:
Cancel common factors:

The numerator y(y-6) in the first expression cancels with the denominator y(y) in the third expression.

Step 3:
Multiply and combine like terms:

Now we can multiply the remaining factors: (y-6)(y-4)(y+7)/(y+6)²