Question 132

What is the simplified value of $$\ [\frac{(1+x^{3})}{(x^{2}-1)}\div\frac{(x^{2}+1-x)}{(x+1)}] \times (x-1)$$?

Solution

Expression = $$\ [\frac{(1+x^{3})}{(x^{2}-1)}\div\frac{(x^{2}+1-x)}{(x+1)}]\times(x-1)$$

= $$[\frac{1+x^3}{(x-1)(x+1)}\times\frac{x+1}{x^2+1-x}](x-1)$$

= $$[\frac{(x+1)(x^2+1-x)}{(x-1)}\times\frac{1}{(x^2+1-x)}](x-1)$$

= $$\frac{(x+1)}{(x-1)}\times(x-1)=(x+1)$$

=> Ans - (C)

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