We have to simplify: (x^2-5x)/(x^2-4x-5)

(x^2-5x)/(x^2-4x-5)

=> x(x - 5)/(x^2 - 5x + x - 5)

=> x(x - 5)/(x(x - 5) + 1(x - 5))

=> x(x - 5)/(x + 1)(x - 5)

=> x/(x + 1)

**The simplified form is x/(x + 1)**

We'll factor the numerator by x:

x(x-5)/(x^2-4x-5)

Since a quadratic may be written as a product of linear factors, when it's roots are determined, we'll find out the roots of denominator:

x^2 - 4x - 5 = 0

We know that a quadratic may be written when knowing the sum and the product of the roots:

x^2 - Sx + P = 0

Comparing, we'll get:

S = 4 and P = -5 => the roots are x1 = 5 and x2 = -1

x^2 - 4x - 5 = (x-5)(x+1)

We'll re-write the fraction:

x(x-5)/(x-5)(x+1)

We'll divide numerator and denominator by (x-5)

x/(x+1)

The given fraction simplified to the lowest terms is x/(x+1).