5/x-1 – 12/x²-1 = 1

My mistake

at first I didn’t see the negative sign and I thought the 12 was positive.

The right way to do it

5(x+1) – 12 = (x-1)(x+1)

5x + 5 – 12 = x²-1

          5x – 7 = x + 1

factor

(x-2)(x-3)= 0

x=2 x=3

Example two

7/x-3 – 4/x = 1

 

Multiply each term by :

 

7x – 4(x-3) = x(x-3)

 

Expand:

 

7x – 4x + 12 = x²- 3x

 

Simplify:

 

3x + 12 = x² – 3x

 

Move everything to one side:

 

0 = x² – 6x – 12