+0

(x+1)/(2x-2)-(x-1)/(2x+2)-(4x)/(x^2-1)+(x^2+1)/(x^2-1)=(x-1)/(x+1) why?

0
286
1
+4

(x+1)/(2x-2)-(x-1)/(2x+2)-(4x)/(x^2-1)+(x^2+1)/(x^2-1)=(x-1)/(x+1)

Arman  Apr 3, 2015

#2
+91513
+10

I made an error is my first post so I have done it again

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

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

Melody  Apr 4, 2015
Sort:

#2
+91513
+10

I made an error is my first post so I have done it again

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

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

Melody  Apr 4, 2015

12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details