Alg1.2.13

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Simplify \frac{3}{x-1}-\frac{2}{x}+\frac{x+3}{(x+1)(x-1)}\,

\frac{3}{x-1}-\frac{2}{x}+\frac{x+3}{(x+1)(x-1)}=\frac{3x(x+1)-2(x-1)(x+1)+(x+3)x}{(x-1)x(x+1)}\,

\frac{3x^2+3x-2x^2+2+x^2+3x}{(x-1)x(x+1)}\,

\frac{2x^2+6x+2}{x^3-x}\,


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