Simplify using partial fractions: 3/(x^2-5x -50).

The denominator x^2 - 5x - 50 can be factorized
as:

x^2 - 5x - 50

=> x^2 - 10x +
5x - 50

=> x(x - 10) + 5(x -
10)

=> (x + 5)(x - 10)

The
denominator has the roots x = -5 and x = 10

Now to find the partial
fractions of 3/(x^2-5x -50), we can use this method.

The partial
fractions are A / (x + 5) + B/(x - 10)

To determine A, cover x + 5
and substitute in 3/(x - 10) the value of the root due to x + 5 , or x =
-5

we get 3/(-5 - 10) = -3/15 =
-1/5

Similarly for B, cover x - 10 and substitute in 3/(x + 5) the
root due to x - 10 or x = 10

we get 3/(5 + 10) =
1/5

The partial fractions of 3/(x^2-5x -50) are 1/5*(x
-10) - 1/5*(x + 5)