FUNKCJA WYMIERNA
Określ dziedzinę wyrażeń i wykonaj działania:
a) 9x² + 6x + 4 8-27x³
4-9x² : (3x-2)³ =
b) 4-x 3-x
4+x - 3+x =
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a)
![\frac{9x^2 + 6x + 4}{4-9x^2}:\frac{8-27x^3}{(3x-2)^3} \frac{9x^2 + 6x + 4}{4-9x^2}:\frac{8-27x^3}{(3x-2)^3}](https://tex.z-dn.net/?f=%5Cfrac%7B9x%5E2+%2B+6x+%2B+4%7D%7B4-9x%5E2%7D%3A%5Cfrac%7B8-27x%5E3%7D%7B%283x-2%29%5E3%7D)
![4-9x^2 \neq 0 4-9x^2 \neq 0](https://tex.z-dn.net/?f=4-9x%5E2+%5Cneq+0)
![(2-3x)(2+3x)\neq 0 (2-3x)(2+3x)\neq 0](https://tex.z-dn.net/?f=%282-3x%29%282%2B3x%29%5Cneq+0)
i ![2+3x \neq 0 2+3x \neq 0](https://tex.z-dn.net/?f=2%2B3x+%5Cneq+0)
i ![3x \neq-2 3x \neq-2](https://tex.z-dn.net/?f=3x+%5Cneq-2)
i ![x \neq-\frac{2}{3} x \neq-\frac{2}{3}](https://tex.z-dn.net/?f=x+%5Cneq-%5Cfrac%7B2%7D%7B3%7D)
![8-27x^3 \neq 0 8-27x^3 \neq 0](https://tex.z-dn.net/?f=8-27x%5E3+%5Cneq+0)
![2^3-(3x)^3 \neq 0 2^3-(3x)^3 \neq 0](https://tex.z-dn.net/?f=2%5E3-%283x%29%5E3+%5Cneq+0)
![(2-3x)(9x^2+6x+4) \neq 0 (2-3x)(9x^2+6x+4) \neq 0](https://tex.z-dn.net/?f=%282-3x%29%289x%5E2%2B6x%2B4%29+%5Cneq+0)
![2-3x \neq 0 2-3x \neq 0](https://tex.z-dn.net/?f=2-3x+%5Cneq+0)
![x \neq \frac{2}{3} x \neq \frac{2}{3}](https://tex.z-dn.net/?f=x+%5Cneq+%5Cfrac%7B2%7D%7B3%7D)
![(3x-2)^3 \neq 0 (3x-2)^3 \neq 0](https://tex.z-dn.net/?f=%283x-2%29%5E3+%5Cneq+0)
![3x-2 \neq 0 3x-2 \neq 0](https://tex.z-dn.net/?f=3x-2+%5Cneq+0)
![3x \neq 2 3x \neq 2](https://tex.z-dn.net/?f=3x+%5Cneq+2)
![x \neq \frac{2}{3} x \neq \frac{2}{3}](https://tex.z-dn.net/?f=x+%5Cneq+%5Cfrac%7B2%7D%7B3%7D)
, ![x \neq \frac{2}{3} x \neq \frac{2}{3}](https://tex.z-dn.net/?f=x+%5Cneq+%5Cfrac%7B2%7D%7B3%7D)
![\frac{9x^2 + 6x + 4}{4-9x^2}:\frac{8-27x^3}{(3x-2)^3}=\frac{9x^2 + 6x + 4}{(2-3x)(2+3x)}:\frac{(2-3x)(9x^2+6x+4)}{(3x-2)^3}= \frac{9x^2 + 6x + 4}{4-9x^2}:\frac{8-27x^3}{(3x-2)^3}=\frac{9x^2 + 6x + 4}{(2-3x)(2+3x)}:\frac{(2-3x)(9x^2+6x+4)}{(3x-2)^3}=](https://tex.z-dn.net/?f=%5Cfrac%7B9x%5E2+%2B+6x+%2B+4%7D%7B4-9x%5E2%7D%3A%5Cfrac%7B8-27x%5E3%7D%7B%283x-2%29%5E3%7D%3D%5Cfrac%7B9x%5E2+%2B+6x+%2B+4%7D%7B%282-3x%29%282%2B3x%29%7D%3A%5Cfrac%7B%282-3x%29%289x%5E2%2B6x%2B4%29%7D%7B%283x-2%29%5E3%7D%3D)
![\frac{9x^2 + 6x + 4}{(2-3x)(2+3x)}\cdot \frac{(3x-2)^3}{(2-3x)(9x^2+6x+4)}=\frac{-(2-3x)^3}{(2-3x)^2(2+3x)} \frac{9x^2 + 6x + 4}{(2-3x)(2+3x)}\cdot \frac{(3x-2)^3}{(2-3x)(9x^2+6x+4)}=\frac{-(2-3x)^3}{(2-3x)^2(2+3x)}](https://tex.z-dn.net/?f=%5Cfrac%7B9x%5E2+%2B+6x+%2B+4%7D%7B%282-3x%29%282%2B3x%29%7D%5Ccdot+%5Cfrac%7B%283x-2%29%5E3%7D%7B%282-3x%29%289x%5E2%2B6x%2B4%29%7D%3D%5Cfrac%7B-%282-3x%29%5E3%7D%7B%282-3x%29%5E2%282%2B3x%29%7D)
![\frac{-(2-3x)}{2+3x}=\frac{3x-2}{3x+2} \frac{-(2-3x)}{2+3x}=\frac{3x-2}{3x+2}](https://tex.z-dn.net/?f=%5Cfrac%7B-%282-3x%29%7D%7B2%2B3x%7D%3D%5Cfrac%7B3x-2%7D%7B3x%2B2%7D)
![\frac{4-x}{4+x}-\frac{3-x}{3+x} \frac{4-x}{4+x}-\frac{3-x}{3+x}](https://tex.z-dn.net/?f=%5Cfrac%7B4-x%7D%7B4%2Bx%7D-%5Cfrac%7B3-x%7D%7B3%2Bx%7D)
![4+x \neq 0 \Rightarrow x \neq -4 4+x \neq 0 \Rightarrow x \neq -4](https://tex.z-dn.net/?f=4%2Bx+%5Cneq+0+%5CRightarrow+x+%5Cneq+-4)
![3+x \neq 0 \Rightarrow x \neq -3 3+x \neq 0 \Rightarrow x \neq -3](https://tex.z-dn.net/?f=3%2Bx+%5Cneq+0+%5CRightarrow+x+%5Cneq+-3)
![\frac{4-x}{4+x}-\frac{3-x}{3+x}=\frac{(4-x)(3+x)}{(4+x)(3+x)}-\frac{(3-x)(4+x)}{(3+x)(4+x)}= \frac{4-x}{4+x}-\frac{3-x}{3+x}=\frac{(4-x)(3+x)}{(4+x)(3+x)}-\frac{(3-x)(4+x)}{(3+x)(4+x)}=](https://tex.z-dn.net/?f=%5Cfrac%7B4-x%7D%7B4%2Bx%7D-%5Cfrac%7B3-x%7D%7B3%2Bx%7D%3D%5Cfrac%7B%284-x%29%283%2Bx%29%7D%7B%284%2Bx%29%283%2Bx%29%7D-%5Cfrac%7B%283-x%29%284%2Bx%29%7D%7B%283%2Bx%29%284%2Bx%29%7D%3D)
![\frac{12+4x-3x-x^2-(12+3x-4x-x^2)}{(3+x)(4+x)}= \frac{12+4x-3x-x^2-(12+3x-4x-x^2)}{(3+x)(4+x)}=](https://tex.z-dn.net/?f=%5Cfrac%7B12%2B4x-3x-x%5E2-%2812%2B3x-4x-x%5E2%29%7D%7B%283%2Bx%29%284%2Bx%29%7D%3D)
![\frac{12+4x-3x-x^2-12-3x+4x+x^2}{(3+x)(4+x)}= \frac{12+4x-3x-x^2-12-3x+4x+x^2}{(3+x)(4+x)}=](https://tex.z-dn.net/?f=%5Cfrac%7B12%2B4x-3x-x%5E2-12-3x%2B4x%2Bx%5E2%7D%7B%283%2Bx%29%284%2Bx%29%7D%3D)
![\frac{2x}{(3+x)(4+x)} \frac{2x}{(3+x)(4+x)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B%283%2Bx%29%284%2Bx%29%7D)
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