JAMB 1991 · UME · Q25✱✱

Evaluate $x^2(x^2 - 1)^{-\frac12} - (x^2 - 1)^{\frac12}$ .

Worked solution (try it first)

Write the second term with the same factor: $(x^2 - 1)^{\frac12} = (x^2 - 1) \times (x^2 - 1)^{-\frac12}$ .
Take out $(x^2 - 1)^{-\frac12}$ : the expression is $(x^2 - 1)^{-\frac12}\left[x^2 - (x^2 - 1)\right]$ .
The bracket is $x^2 - x^2 + 1 = 1$ , so the result is $(x^2 - 1)^{-\frac12}$ , option D.