((y+2)/(y^2-49))subtract ((y)/(y^2+6y-7))
The directions are simplify and subtract
(y+2)
-----------
(y-7)(y+7)
-
y
-----------------
(y+7)(y-1)
which you need an LCD for
(y+2) (y-1)
---------------
(y-7)(y+7)(y-1)
-
y (y-1)(y-7)
-----------------
(y+7)(y-1)(y-7)
y+7
you forgot that pesky "y" upstairs...
y/(y+7)
To simplify and subtract the given expression ((y+2)/(y^2-49)) subtract ((y)/(y^2+6y-7)), let's break it down step by step:
Step 1: Factor the denominators of both fractions:
Denominator of the first fraction, y^2-49, is a difference of squares and can be factored as (y-7)(y+7).
Denominator of the second fraction, y^2+6y-7, cannot be factored further.
Step 2: Rewrite the expression with the factored denominators:
((y+2)/[(y-7)(y+7)]) - (y/(y^2+6y-7))
Step 3: Find the least common denominator (LCD) of the fractions. Since the denominators have no common factors, the LCD is simply the product of the two denominators: (y-7)(y+7)(y^2+6y-7).
Step 4: Multiply the numerators of each fraction by the necessary factors to obtain the common denominator (LCD):
[(y+2)(y^2+6y-7)]/[(y-7)(y+7)(y^2+6y-7)] - [(y)(y-7)]/[(y-7)(y+7)(y^2+6y-7)]
Step 5: Combine the numerators over the LCD:
[(y^3+6y^2-7y+2)-(y^2-7y)]/[(y-7)(y+7)(y^2+6y-7)]
Step 6: Simplify the numerator by combining like terms:
[y^3+6y^2-7y+2-y^2+7y]/[(y-7)(y+7)(y^2+6y-7)]
Step 7: Further simplify the numerator:
[y^3+5y^2+2]/[(y-7)(y+7)(y^2+6y-7)]
Therefore, the simplified and subtracted expression is (y^3+5y^2+2)/[(y-7)(y+7)(y^2+6y-7)].