How can you evaluate (x)/(x^2-4) - (2)/(x^2-4)xx242x24?

1 Answer

=color(blue)(1/(x+2)=1x+2

with exclusion x != 2x2

Explanation:

(x)/(x^2-4) - (2)/(x^2-4) xx242x24

Here the denominators are the same, so combining the numerators we get:

(x- 2)/(x^2-4) x2x24

As per property:
color(blue)(a^2-b^2) = (a+b)(a-b)a2b2=(a+b)(ab)

Similarly :
color(blue)((x^2-4)) =(x+2)(x-2) (x24)=(x+2)(x2)

Expressing the denominator in the this way, the expression becomes:

cancel(x- 2)/color(blue)((x+2)cancel((x-2))

=color(blue)(1/(x+2)

with exclusion x != 2