If x > 2, then x² - x - 6/x² - 4 =

Solution:

It is given that equation is

(x² - x - 6)/(x² - 4)

By splitting the middle term we get

= (x² - 3x + 2x - 6)/ (x² - 4)

Using the algebraic identity

a² - b² = (a + b) (a - b)

= (x² - 3x + 2x - 6)/ (x + 2) (x - 2)

Taking out the common terms

= [x(x - 3) + 2(x - 3)]/ (x + 2)(x - 2)

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

So we get

= (x - 3)/ (x - 2)

Therefore, x² - x - 6/x² - 4 = (x - 3)/ (x - 2).

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If x > 2, then x² - x - 6/x² - 4 =

Summary:

If x > 2, then x² - x - 6/x² - 4 = (x - 3)/ (x - 2).