SKRACANIE WYRAŻEŃ WYMIERNYCH

30 2*3*5 5

---- = --------- = ---

42 2*3*7 7

2a²b 2a*a*b a

= =

6ab² 2*3a*b*b 3b

x³-x y² x(x²- y²) x(x- y)(x+ y) x+y

-------- = ------------ = ----------------- = --------

x²y-x y² xy(x- y) xy(x- y) y

ROZSZERZANIE WYRAŻEŃ WYMIERNYCH

przez 4

2 2*4 8

---- = ------ = ---

3 3*4 12

przez (-4ac²)

2ab 2a*b(-4ac²) -8a³bc²

= =-----------

3c 3c (-4ac²) -12ac³

^{przez x-3}

2x- 1 (2x-1)(x- 3) 2x²-7x+3

-------- = ------------ = -----------------

x+3 (x+3) (x- 3) x²- 9

DODAĆ WYRAŻENIA WYMIERNRE

3 5 9 10 9+10 19

--- + ---- = --- + ---- = ------- = ------

4 6 12 12 12 12

a b a² cb² a²+ b²c

--- + ---= ----- +-------- = -------

bc a abc abc abc

x² x x 1

-------- +------- = ---------- + -------------- =

2x-2 x²- 1 2(x- 1) (x-1)( x+1)

x(x+1) 2 x(x+1)+2

--------------- + ---------------- = -----------------=

2(x-1)(x+1) 2(x-1) (x+1) 2(x-1) (x+1)

x²+x+2

= ----------------

2(x-1) (x+1)

ODEJMOWANIE WYRAŻEŃ WYMIERNYCH

7 1 21 4 21-4 17

--- - ---- = --- - ---- = ------- = ------

8 6 24 24 24 24

a b a² b² a²- b²

--- - ---= ----- - -------- = -------

b a ab ab ab

1 y 1 y

-------- - ------- = ---------- - -------------- =

x-y x²- xy x- y x ( x+y)

x(x+y) x(x-y) x(x+y) -y(x-y)

--------------- - ---------------- = -----------------=

x(x-y)(x+y) x(x-y)(x+y) x(x-y)(x+y)

x²+xy-xy+ y² x²- y²

= ------------------ = -----------

x(x-y)(x+y) x(x²+ y²)

(2x⁴ +3x³-6x²+8x-8): (x²+2x-3)=2x²-x+2

2x⁴ +4x³-6x²

-x³ +0x²+8x-8

-x³ - 2x²+3x

2x²+5x- 8

2x²+4x- 6

x - 2

x²+4y²= -x²-4xy-4y² -2x²+8xy-8y² = -3x²+4xy-12y²

Dodawanie wielomianów

3x⁴+x³-5x+2 i 2x³-7x²+x-4

(3x⁴+x³-5x+2)+(2x³-7x²+x-4)

3x⁴+x³-5x+2+2x³-7x²+x-4=

3x⁴+x³+2x³-7x²+-5x+x-4+2=

3x⁴+3x³-7x²-4x-2

Odejmowanie wielomianów

4x³+3x²-x-5 i 2x²-6x+4

(4x³+3x²-x-5)-( 2x²-6x+4)=

(4x³+3x²-x-5)+( -2x²+6x-4)=

4x³+3x²-x-5-2x²+6x-4)=

4x³+3x²-2x²-x+6x-5-4=

4x³+(3-2)x²+(-1+6)x+(-5-4)=

4x³+x²+5x-9

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