x squared minus 4 times x minus 12 over 36 minus x squared?

Hi,

x² - 4x - 12
--------------- =
36 - x²

(x - 6)(x + 2)
----------------- =
(6 - x)(6 + x)

Since (x - 6) and (6 - x) are opposite factors, they cancel leaving a -1 one place and a 1 the other place.

-1(x + 2)
------------ =
1(6 + x)

-x - 2
-------- <==ANSWER
6 + x

I hope that helps!! :-)

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

(x - 12) cannot be factored

Rewriting the denominator as

(36 - x^2) = -(x^2 - 36) = -(x+6)(x-6)

The fraction becomes

[(x+2)(x-2)(x-12)]/[-(x+6)(x-6)]

No cancellation is possible

Assuming you mean :-

(x² - 4)(x - 12)
---------------------
36 - x²

(x - 2)(x + 2)(x - 12)
----------------------------
(6 - x)(6 + x)

you are able to remedy this via applying the quadratic formula. ie x = [-b (+ or -) sq. root(b^2 - 4ac)] / 2a for this reason a = 9, b = -18 and c =3 entering into those values into the formula would desire to offer you [-18 (+ or -) sq. root(216)] / 18 which while simplified is a million (+ or -) 0.81649 ie a million (+ or -) sq. root of 6 over 3

[x^2 - 4][(x - 12)/(36 - x^2)]
= [(x + 2)(x - 2)][(x - 12)/(6 + x)(6 - x)]
= (x - 12)(x + 2)(x - 2)/(6 + x)(6 - x)

[(x-6)(x+2)]/[(6+x)(6-x)]

(x² -4x -12)/( 36 - x²)...........factorise both

(x² -4x -12)............(x - 6)(x + 2)
( 36 - x²)...........(6 - x)( x + 6 ) = -(x -6)(x + 6)

eliminate (x - 6) top and bottom

so
(x + 2)/-(6 + x)

Tidy to

-(x + 2)
----------
(x + 6)

;-) PS Need to have better question writing
Copy the Script (x²) and paste it into Word and save it ~ for next time you need x²