Question

Help
Write as a single fraction.
Simplify your answer as much as possible.

Answer 1

Combining the fractions involves finding a common denominator, adjusting numerators, and simplifying. The result is (4
`u^2` + 5u - 51)/((u-7)(u+3)(u-3)).

To combine the given fractions 5/(u-7) + u/(
`u^2`-9) + 2/(u-3), find a common denominator. The common denominator is (u-7)(u+3)(u-3). Adjust the numerators accordingly:

5(u+3)/((u-7)(u+3)(u-3)) + u(u-7)/((u-7)(u+3)(u-3)) + 2(u+3)/((u-7)(u+3)(u-3)).

Combine the numerators:

(5(u+3) + u(u-7) + 2(u+3))/((u-7)(u+3)(u-3)).

Expand and simplify the numerator:

(5u + 15 +
`u^2` - 7u + 2u + 6)/((u-7)(u+3)(u-3)).

Combine like terms:

(4
`u^2` + 5u - 51)/((u-7)(u+3)(u-3)).

Thus, the combined fraction is (4
`u^2`+5u-51)/((u-7)(u+3)(u-3)).