Question

RATIONAL EXPRESSION HELP X/X^2-1+6X/X-X^2

Answer 1

Factor denominators
\[\frac{x}{(x+1)(x-1)} + \frac{6x}{x(1-x)}\]
cancel x"s .... pull out a neg from 2nd denominator
\[\frac{x}{(x+1)(x-1)} - \frac{6}{x-1}\]
Notice both denominators share the factor (x-1)
To make denominators the same multiply 2nd fraction by (x+1)/(x+1)
\[\frac{x}{(x+1)(x-1)} - \frac{6(x+1)}{(x+1)(x-1)}\]
Now combine fractions... add like terms on top
\[\frac{x -6x-6}{(x+1)(x-1)}\]
\[\frac{-5x-6}{(x+1)(x-1)}\]