((y+2)/(y^2-49))subtract ((y)/(y^2+6y-7))
subtract and simplify ,,,,,i know i need to find LCD which is y+7,and multiply both sides to get it that way i think answer is -6y-2/y+7....is this right???
As I showed you below the LCD is
(y-7)(y+7)(y-1)
To subtract and simplify the expression ((y+2)/(y^2-49)) - ((y)/(y^2+6y-7), you correctly identified that the first step is to find the least common denominator (LCD). The LCD is the smallest expression that both denominators, (y^2-49) and (y^2+6y-7), can divide evenly into.
To find the LCD, you can factor the denominators:
y^2-49 = (y+7)(y-7)
y^2+6y-7 = (y-1)(y+7)
The LCD will be the product of each unique factor raised to its highest power:
LCD = (y+7)(y-7)(y-1)
Now, you can multiply each term by the necessary factors to obtain the LCD. The first term, ((y+2)/(y^2-49)), already has the factor of (y+7) in the denominator, so you only need to multiply the numerator by (y-1):
((y+2)/(y^2-49)) * ((y-1)/(y-1))
The second term, ((y)/(y^2+6y-7)), already has all the factors of the LCD in the denominator, so you don't need to multiply anything additional to this term.
After multiplying the numerators, the expression becomes:
((y+2)(y-1))/((y+7)(y-7)(y-1)) - (y)/(y^2+6y-7)
Now, you can combine the terms over the common denominator:
((y+2)(y-1) - y(y+7))/((y+7)(y-7)(y-1))
Next, expand the numerator and simplify:
(y^2 + y - 2 - y^2 - 7y)/((y+7)(y-7)(y-1))
(y^2 - 6y - 2)/((y+7)(y-7)(y-1))
Therefore, the simplified expression is (y^2 - 6y - 2)/((y+7)(y-7)(y-1)). It seems there was an error in your solution. The correct answer is not -6y-2/(y+7).