Question

How do I simplify: (x^2-6x+8/2x^2-7x+6) - (x^2-x-12/2x^2-5x-12)?

Answer 1

x^2-6x+8 x^2-x-12
--------- - ----------
2x^2-7x+6 2x^2-5x-12

= (x-4)(x-2) (x-4)(x+3)
---------- - ---------
(2x-3)(x-2) (2x+3)(x-4)

= (x-4)(2x+3) (x-4)(x+3)
----------- - ----------
(2x-3)(2x+3) (2x+3)(2x-3)

= (x-4)(2x+3) - (x+3)(2x-3)
-------------------------
(2x-3)(2x+3)

= 2x^2-5-12- (2x^2+3x-9)
---------------------------
(2x-3)(2x+3)

= -5x-12-3x+9
-------------
(2x-3)(2x+3)

= -8x-3
-----------
(2x-3)(2x+3)

Is this right?

Answer 2

No, let me write it
x^2-6x+8 x^2-x-12
--------- - ---------- (1)
2x^2-7x+6 2x^2-5x-12

= (x-4)(x-2) (x-4)(x+3)
---------- - --------- (2)
(2x-3)(x-2) (2x+3)(x-4)

so far so good, but now we should notice that x-2 cancels in this first expression... (continued)

Answer 3

and the x+4 in the second, giving\[{x−4\over2x+3}−{x+3\over2x+3}={x−4−x−3\over2x+3}={−7\over2x+3}\]which is your answer

Answer 4

ohhh...

Answer 5

really?