How do you simplify this fraction? I need the work.

x^2 - x - 6
--------------
x^2 - 4

factor both the top and bottom...
(x+2)(x-3) divided by (x+2)(x-2)

cancel out common factor (x+2) on top and bottom

so the simplified fraction is:
(x-3)/(x-2)

Numerator = x^2 -x - 6 = x^2 - 3x +2x -6 = x(x-3) +2(x-3)
= (x+2)(x-3)
Denominator, x^2 -4 =(x-2)(x+2)

The whole expression= Numerator/ Denominator
= (x+2)(x-3)/ (x-2)(x+2)
= (x-3)/(x-2) is the answer

for numerator
factorizing we get X^2-3X+2X-6
=X(X-3)+2(X-3)
=(X+2)(X-3)
for denumerator
factorizing=X^2-4
=X^2-2^2
=(X+2)(X-2)

now it all become
(X+2)(X-3)/(X+2)(X-2)
(X-3)/(X-2) is the required answer

x^2 - x - 6
--------------
x^2 - 4

Factor

(x+2)(x-3)
---------------
(x-2)(x+2)

Cross out (x+2) because it cancels out

x-3
----- <--- This is your answer!
x-2

(x^2 - x - 6)/(x^2 - 4)

((x - 3)(x + 2))/((x - 2)(x + 2))

(x - 3)/(x - 2)