Question

Simplify the following rational function: 3/x+1+x/x-1

Answer 1

\[\large \frac{3}{x+1}+\frac{x}{x-1}\]


\[\large \frac{3(x-1)}{(x+1)(x-1)}+\frac{x}{x-1}\]


\[\large \frac{3x-3}{(x+1)(x-1)}+\frac{x}{x-1}\]


\[\large \frac{3x-3}{(x+1)(x-1)}+\frac{x(x+1)}{(x+1)(x-1)}\]


\[\large \frac{3x-3}{(x+1)(x-1)}+\frac{x^2+x}{(x+1)(x-1)}\]


\[\large \frac{3x-3+x^2+x}{(x+1)(x-1)}\]


\[\large \frac{x^2+4x-3}{(x+1)(x-1)}\]
So \[\large \frac{3}{x+1}+\frac{x}{x-1}=\frac{x^2+4x-3}{(x+1)(x-1)}\]

Answer 2

thanks!