Question

Subtract:

4x by x² - 1 - x + 1 by x - 1.

Answer 1

\(\frac{4x}{x^2-1}-\frac{x+1}{x-1}\)

\(=\frac{4x-(x+1)^2}{x^2-1}\)

\(=\frac{4x-(x^2+2x+1)}{x^2-1}\) 

\(=\frac{-(x^2+2x+1-4x)}{x^2-1}\)

\(=-\frac{x^2-2x+1}{x^2-1}\) 

\(=-\frac{(x-1)^2}{x^2-1}\) 

\(=\frac{(x-1)^2}{1-x^2}\)