Question

adding or subtracting radical expressions with denominators 1/x+1 + x/x-6 -5x-2/x^2-5x-6

Answer 1

Factor out the bottom of the large radical into (x+1)(x-6) then multiply across both of the other terms to get a common denominator then simply add and subtract the numerator.

Answer 2

Do you mean:\[\frac{1}{x+1}+\frac{x}{x-6}-\frac{5x-2}{x^2-5x-6}\]

If so then this is the same as:
\[\frac{x-6}{(x+1)(x-6)}+\frac{x(x+1)}{(x+1)(x-6)}-\frac{5x-2}{x^2-5x-6}=\frac{x^2-3x-4}{(x+1)(x-6)}=\frac{(x-4)(x+1)}{(x+1)(x-6)}\frac{x-4}{x-6}\]

Answer 3

\[=\frac{x-4}{x-6}\]

Answer 4

\[=\frac{(x-6)+2}{x-6}=1+\frac{2}{x-6}\]

Answer 5

yes