Add or Subtract as Indicated; Then Use Fundamental Identities to Simplify

Multiple Choice

Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$$\sin x + 1 + \frac { 1 } { \sin x - 1 }$$

A) $\frac { \sin ^ { 2 } x } { \sin x - 1 }$

B) $\frac { 1 - \cos ^ { 2 } x } { \sin x - 1 }$

C) $\frac { 1 + \cos ^ { 2 } x } { \sin x - 1 }$

D) $\frac { \sec x - \cos x } { \tan x - \sec x }$

E) $\frac { \csc x - \cot x \cos x } { 1 - \csc x }$