wyrazenie
ps. pozdro dla Marco12
3x +1 2x-1 (3x+1)(x+3) - (2x-1)(x-2) 3x²+9x +x +3 -2x²+4x +x -2
--------- - --------- = ----------------------------------- = --------------------------------------- =
x -2 x +3 (x-2)(x+3) (x-2)(x+3)
x² + 15x +1
= ------------------
(x-2)(x+3) Zał. x-2 ≠ 0 ⇒ x ≠ 2
x+3 ≠0 ⇒ x ≠ -3
Czyli D = R \ {-3, 2 }
(3x+1)/(x-2) - (2x-1)/(x+3) = zał.x∈R\{-3,2}
=(3x+1)(x+3)/(x-2)(x+3) - (2x-1)(x-2)/(x-2)(x+3)=
=[(3x²+9x+x+3)- (2x²-4x-x+2)]/(x-2)(x+3)=
=(x²+15x+1)/(x-2)(x+3) =
=(x²+15x +1)/(x²+x-6)
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3x +1 2x-1 (3x+1)(x+3) - (2x-1)(x-2) 3x²+9x +x +3 -2x²+4x +x -2
--------- - --------- = ----------------------------------- = --------------------------------------- =
x -2 x +3 (x-2)(x+3) (x-2)(x+3)
x² + 15x +1
= ------------------
(x-2)(x+3) Zał. x-2 ≠ 0 ⇒ x ≠ 2
x+3 ≠0 ⇒ x ≠ -3
Czyli D = R \ {-3, 2 }
(3x+1)/(x-2) - (2x-1)/(x+3) = zał.x∈R\{-3,2}
=(3x+1)(x+3)/(x-2)(x+3) - (2x-1)(x-2)/(x-2)(x+3)=
=[(3x²+9x+x+3)- (2x²-4x-x+2)]/(x-2)(x+3)=
=(x²+15x+1)/(x-2)(x+3) =
=(x²+15x +1)/(x²+x-6)