Simplify to the lowest terms (x^2-5x)/(x^2-4x-5)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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