find the domain of original expression and simplify
y^2-16/3y+12
To find the domain of the expression, we need to find all the possible values that y can take while still resulting in a valid expression.
The expression is (y^2 - 16)/(3y + 12).
The denominator 3y + 12 cannot be zero because division by zero is undefined. Therefore, we need to find the values of y that satisfy 3y + 12 ≠ 0.
Subtracting 12 from both sides of the inequality gives us 3y ≠ -12.
Dividing both sides of the inequality by 3 gives us y ≠ -4.
So, the domain of the original expression is all real numbers except -4.
To simplify the expression:
We can factor the numerator: y^2 - 16 = (y - 4)(y + 4).
The expression becomes ((y - 4)(y + 4))/(3y + 12).
Since (y + 4)/(3y + 12) cannot be further simplified, the simplified expression is: (y - 4)(y + 4)/(3y + 12).
find the domain of original expression
y^2-16/3y+12
To find the domain of the original expression, we need to determine the values that y cannot take, as these values would result in division by zero.
In this case, we need to determine when the denominator, 3y + 12, is equal to zero.
3y + 12 = 0
Subtracting 12 from both sides gives: 3y = -12
Dividing both sides by 3 gives: y = -4
Therefore, y cannot be equal to -4 since it would result in division by zero.
Hence, the domain of the original expression is all real numbers except -4.
To find the domain of the expression `(y^2-16)/(3y+12)`, we need to determine the values of `y` that would cause the denominator to be zero. Division by zero is undefined.
Setting the denominator to zero:
3y + 12 = 0
Subtracting 12 from both sides:
3y = -12
Dividing both sides by 3:
y = -4
So, the value `y = -4` causes the denominator to be zero. Therefore, the domain of the expression is all real numbers except for `-4`.
To simplify the expression, we can factor the numerator and factor out the greatest common factor from the numerator and denominator.
Factoring the numerator:
(y^2 - 16) = (y-4)(y+4)
So, the expression becomes:
(y-4)(y+4)/(3y+12)
Now, we can simplify further by factoring out the greatest common factor:
(y-4)(y+4)/(3(y+4))
Simplifying, we get:
(y-4)/3