Simplify:
9/(y+8)-y/(y-2)+(y^2+4)/(y^2+6y-16)
IS the answer y-14/(y-2)(y+8)?
yes
To simplify the given expression, we need to combine the fractions and then simplify the resulting expression.
Let's work through it step by step:
1. Start with the given expression: 9/(y+8) - y/(y-2) + (y^2+4)/(y^2+6y-16)
2. Find a common denominator:
The denominators of the fractions in the expression are (y+8), (y-2), and (y^2+6y-16). To find a common denominator, we need to factor the last denominator: y^2 + 6y - 16.
Factoring (y^2+6y-16), we get:
(y+8)(y-2)
Therefore, the common denominator is (y+8)(y-2).
3. Rewrite the fractions with the common denominator:
9(y-2)/[(y+8)(y-2)] - y(y+8)/[(y+8)(y-2)] + (y^2+4)/[(y+8)(y-2)]
4. Combine the fractions:
(9(y-2) - y(y+8) + (y^2+4))/[(y+8)(y-2)]
5. Simplify the numerator:
Expanding and combining like terms in the numerator:
(9y - 18 - y^2 - 8y + y^2 + 4)/[(y+8)(y-2)]
(-9y - 14)/[(y+8)(y-2)]
6. Final simplified expression:
-(9y + 14)/[(y+8)(y-2)]
Therefore, the simplified expression is -(9y + 14)/[(y+8)(y-2)], which is different from the answer you provided.