6-y/y^2-2y-24=?
*I don't get it at all!!!
Answered in another post.
To solve the expression 6 - y/y^2 - 2y - 24, we can follow a specific order of operations called PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
1. First, let's simplify the expression by factoring the denominator: y^2 - 2y - 24. This is a quadratic equation, so we want to find two numbers that multiply to -24 and add up to -2y. By trial and error, we can see that -6 and 4 fit these conditions since (-6) * 4 = -24 and (-6) + 4 = -2.
So we can rewrite the equation as follows: 6 - y/(y - 6)(y + 4) - 24.
2. Now we have a common denominator for the expression, which is (y - 6)(y + 4). To combine the fraction, we need to multiply the first term, 6, by (y + 4), and then subtract the result obtained from the next term, which is - y/(y - 6)(y + 4).
The new expression becomes: (6(y + 4))/(y - 6)(y + 4) - y/(y - 6)(y + 4) - 24.
3. We can now combine the fractions: (6(y + 4) - y)/(y - 6)(y + 4) - 24.
4. Expanding the numerator: (6y + 24 - y)/(y - 6)(y + 4) - 24.
5. Simplifying: (5y + 24)/(y - 6)(y + 4) - 24.
And that is the simplified form of the expression 6 - y/y^2 - 2y - 24.