Question

How solve it?

Answer 1

The limit equals `5`. See below for proof.

Explanation:

Start by factoring and seeing what you can eliminate.

`=>lim_(x->2) (2x^2 - 4x + x - 2)/(x^2(x - 2) - 3(x - 2))`

`=>lim_(x->2) (2x(x - 2) + 1(x - 2))/((x^2 - 3)(x - 2)`

`=>lim_(x->2) ((2x + 1)(x - 2))/((x^2 -3)(x - 2))`

`=>lim_(x->2) (2x + 1)/(x^2 - 3)`

Evaluate through substitution now.

`=>(2(2) + 1)/(2^2 - 3)`

`=>5/1`

`=>5`

Hopefully this helps!