Question

What are the domain restrictions of the expression (y²-3y-40)/y²+9y+20 ？ Select each correct answer.

O y≠ -8
O y≠ -5
O y≠ 8
O y≠ 5
O y≠ 4
O y≠ -4

Answer 1

The domain restrictions of the expression (y²-3y-40)/(y²+9y+20) are y ≠ -5 and y ≠ -4 since those values make the denominator zero and the expression undefined.

Step-by-step explanation:

The domain restrictions of the expression (y²-3y-40)/(y²+9y+20) are determined by the values of y for which the denominator is equal to zero, since division by zero is undefined in mathematics. To find these values, we need to factor the denominator:

y² + 9y + 20 = (y + 5)(y + 4)

Now, setting each factor equal to zero gives us:

• y + 5 = 0 → y = -5
• y + 4 = 0 → y = -4

Therefore, the domain restrictions are y ≠ -5 and y ≠ -4. These are the values that y cannot take, as they would make the denominator of the expression equal to zero.