Question

a) X^2-6x+9
--------------- = < ---- supra
X^2-9

b) x^2+8x+12
-------------- =
X^2+7x+6

c) 4-x^2
-------------- =
X^2-5x+4

d) x^2+3x+4
--------------- =
X^2-5x+4

e) 9-x^2
--------- =
X^2-8x+15

f)x^2-x
-----------
X^2-2x+1

g) x(x-2)+1
-----------
X^2+2x-3

h) x^2-x-6
-----------
(X-4)^2+(x-4)

i) (x-2)^2-x+2
--------------
(X-3) ^2-1
Plssss Ajutor....

Answer 1

a) (x²-6x+9)/(x²-9) =(x-3)²/(x-3)(x+3) =(x-3)/(x+3)

b) (x²+8x+12)/(x²+7x+6)=(x+2)(x+6)/(x+1)(x+6)=(x+2)/(x+1)

c) (4-x²)/(x²-5x+4)=(2-x)(2+x)/(x-4)(x-1)

d) (x²+3x+4)/(x²-5x+4)=(x²+3x+4)/(x-4)(x-1)

 e) (9-x²)/(x²-8x+15)=(3-x)(3+x)/(x-5)(x-3)=(3+x)/(x-5)(-1)=(3+x)/(5-x)

 f)(x²-x)/(x²-2x+1)=x(x-1)/(x-1)²=x/(x-1)

g) [x(x-2)+1]/(x²+2x-3)=(x²-2x+1)/(x²+2x-3)=(x-1)²/(x-1)(x+3)=(x-1)/(x+3)

 h) (x²-x-6)/[(x-4)²+(x-4)]=(x-3)(x+2)/(x²-8x+16+x-4)=(x-3)(x+2)/(x²-7x+12)=
=(x-3)(x+2)/(x-4)(x-3)=(x+2)/(x-4)

 i) [(x-2)²-x+2]/[(x-3)²-1]=(x²-4x+4-x+2)/(x-3-1)(x-3+1)=(x²-5x+6)/(x-4)(x-2)=
=(x-3)(x-2)/(x-4)(x-2)=(x-3)/(x-4)