I need help :C
What is the quotient in simplest form? State any restrictions on the variable.
y^2 - 5y + 6 y^2 + 3y - 10
----------------- / -------------------
y^3 4y^2
I am not certain which is the numerator and which is the denominator. You can start by factoring the two trinomials on top.
I think they are being multiplied together...
Please advise.
Remember to state your restrictions before you reduce any of your expression.
I assume you mean
(y^2-5y+6)/(y^3) + (y^2+3y-10)/(4y^2)
If so, the LCD is 4y^3, so you have
(4(y^2-5y+6) + y(y^2+3y-10))/(4y^3) = (y^3+7y^2-30y+24)/(4y^3)
naturally, y≠0
Of course, I'd be happy to help you! To find the quotient in simplest form, we need to divide the numerator by the denominator. In this case, the numerator is y^2 - 5y + 6, and the denominator is y^3 * 4y^2.
Let's break this down step by step:
Step 1: Simplify the numerator:
The numerator is already in its simplest form. It cannot be factored further.
Step 2: Simplify the denominator:
To simplify the denominator, we can combine the exponents of y.
The denominator can be rewritten as y^(3 + 2) * 4, which is equal to y^5 * 4.
Step 3: Divide the numerator by the denominator:
Now that we have simplified the numerator and denominator, we can perform the division:
(y^2 - 5y + 6) / (y^3 * 4y^2) = (y^2 - 5y + 6) / (4y^5)
Step 4: State any restrictions on the variable:
To determine the restrictions on the variable, we need to consider any values of y that would make the denominator equal to zero. In this case, since the denominator contains y raised to a positive power, there are no restrictions on the variable y.
So, the quotient in simplest form is (y^2 - 5y + 6) / (4y^5), and there are no restrictions on the variable y. I hope this helps! Let me know if you have any further questions.