Simplifying Algebraic Fractions

Question

Simplify

(x^2-5x-6)/(x-1)

Answer 1

The expression is

• Now factorise the numrator of the above fraction.

x² - 5x  - 6

Multiply first term x² and last term -6 = -6x²

The correct pair of the terms -6x and x multiply to -6x² and add to -5x.

Replace the middle term -5x with - 6x + x.

= x² - 6x + x - 6

Group the terms into two pairs.

= (x² - 6x) + (x - 6)

Factor out x from the first group  and factor out 1 from the second group.

= x(x - 6) + 1(x - 6)

Factor out common term x - 6.

= (x - 6)(x + 1)

Subsstitute the numarator value in the fraction.