Final answer:
Simplify the complex fraction by factoring y^(2)-9 into (y-3)(y+3) on the top and simplifying the bottom to a single fraction, then further simplifying by multiplying the top part by the reciprocal of the bottom part.
Step-by-step explanation:
To simplify the complex fraction (5/(y^(2)-9))/(6/(y+3)+1), we first identify that y^(2)-9 is a difference of squares, which can be factored into (y-3)(y+3). This simplifies the top part of the equation to 5/((y-3)(y+3)).
For the bottom part of the equation, we need to simplify it to a single fraction. To achieve this, we find a common denominator for (6/(y+3)) and 1. The common denominator here is (y+3). This simplifies the bottom part of the equation to ((6+ (y+3))/(y+3)).
Finally, you simplify the complex fraction by multiplying the top part of the major fraction by the reciprocal of the bottom part. So, the simplified form is [5(y+3)]/[(y-3)(6+y+3)].
Learn more about Simplifying Complex Fractions