What is wrong with the following equation? x2 + x- 12/x-3= x + 4 (x - 3)(x + 4)

Question

What is wrong with the following equation? x2 + x- 12/x-3= x + 4 (x - 3)(x + 4) x2 + x - 12 The left-hand side is not defined for x =0, but the right-hand side is. The left-hand side is not defined for x = 3, but the right-hand side is. None of these - the equation is correct. In view of part (a), explain why the equation lim x rightarrow 3 x2+x-12/x-3= lim x rightarrow 3 (x+4) is correct. Since x2+x-12/x-3 and x + 4 are both continuous, the equation follows. Since the equation holds for all x 3, it follows that both sides of the equation approach the same limit as x Rightarrow 3. This equation follows from the fact that the equation in part (a) is correct. None of these - the equation is not correct.

Explanation / Answer

Part a) left hand side of the eqn. is equal to zero by zero or (0/0) at x=3 which in itself is undefined, But right hand side of the eqn. = 7 at x=3. Therefore there lies the ambiguity of the value of LHS.

Ans iii) The left hand side is not defined for x=3 but right hand side is.

Part b)

In this part X is tending to 3 but never equal to 3.

So, the value is never 0/0 its some finite value getting cancelled from top and bottom. Therefore both sides approach the same limit for x tending to 3.

Therefore correct answer is ii) Since the eqn. holds for all x not equal to 3, it follows that both sides of the eqn approach the same limit as x tending to 3

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