Problems from Function composition

Given $f (x) = x - 1$ and $g (x) = \frac{x^{2}}{1 - x}$ , find $(f \circ g) (x)$ .

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$(f \circ g) (x) = f (g (x)) = g (x) - 1 = \frac{x^{2}}{1 - x} - 1 = \frac{x^{2} - 1 + x}{1 - x} = \frac{x^{2} + x - 1}{1 - x}$

$(f \circ g) (x) = \frac{x^{2} + x - 1}{1 - x}$

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