y^2-5y over y^2-7y+10 What did I do wrong.. for my answer i got (y+5) over (y-2) and the correct answer is y over (y-2)???
How would you do this problem?
3x over x+1 = ? over x^2-x-2
1) y(y-5)/(y-5)(y-2)= y/(y-2)
I don't understand how you got to that answer
To understand the mistake made in the problem, let's walk through the steps for simplifying the expression y^2-5y over y^2-7y+10.
1. Start with the expression y^2-5y over y^2-7y+10.
2. Factor the numerator and denominator if possible. In this case, the numerator y^2-5y cannot be factored further, but the denominator y^2-7y+10 can be factored as (y-2)(y-5).
3. Rewrite the expression using the factored form of the denominator: y^2-5y over (y-2)(y-5).
4. Notice that both the numerator y^2-5y and the term (y-5) in the denominator have a common factor of y. Factor out y from both: y(y-5) over (y-2)(y-5).
5. Cancel out the common factor of (y-5) in the numerator and denominator: y over (y-2).
Based on the steps mentioned above, the correct simplification of y^2-5y over y^2-7y+10 is indeed y over (y-2).
Now, to solve the problem involving 3x over x+1 = ? over x^2-x-2, you can follow these steps:
1. Start with the equation 3x over x+1 = ? over x^2-x-2.
2. Cross-multiply the equation by multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa. This gives you: (3x)(x^2-x-2) = (?)(x+1).
3. Expand both sides of the equation and simplify: 3x^3-3x^2-6x = ?x+?.
4. At this point, the question mark (?) represents the missing parts of the equation, which need to be determined.
5. Group like terms on both sides of the equation: 3x^3-3x^2-6x - ?x = ?.
6. Combine like terms: 3x^3-3x^2-6x - ?x = ?.
7. On the left side, factor out common factors from the terms: x(3x^2-3x-6-?) = ?.
8. At this stage, it seems like a number or expression is missing from the equation for the factor 3x^2-3x-6-? in brackets. Without knowing the specific value or expression, it is not possible to solve the equation further or determine the missing quantity.
Therefore, you would need additional information to solve the problem completely.