Réitigh 6x-36/x^2-36div12x^2-36x/x^2+9x-36=x+12/2x^2+12x

$$\frac { 6 x - 36 } { x ^ { 2 } - 36 } \div \frac { 12 x ^ { 2 } - 36 x } { x ^ { 2 } + 9 x - 36 } = \frac { x + 12 } { 2 x ^ { 2 } + 12 x }$$

Réitigh do x.

$$x\in \mathrm{R}\setminus 6,-6,0,3,-12$$

Céimeanna gearra réitigh

Ní féidir leis an athróg x a bheith comhionann le haon cheann de na luachanna -6,0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi 2x\left(x+6\right).

$$\frac{1}{6}\left(x+6\right)\left(12+x\right)\times \frac{6x-36}{x^{2}-36}=x+12$$

Úsáid an t-airí dáileach chun \frac{1}{6} a mhéadú faoi x+6.

$$\left(\frac{1}{6}x+1\right)\left(12+x\right)\times \frac{6x-36}{x^{2}-36}=x+12$$

Úsáid an t-airí dáileach chun \frac{1}{6}x+1 a mhéadú faoi 12+x agus chun téarmaí comhchosúla a chumasc.

$$\left(3x+\frac{1}{6}x^{2}+12\right)\times \frac{6x-36}{x^{2}-36}=x+12$$

Úsáid an t-airí dáileach chun 3x+\frac{1}{6}x^{2}+12 a mhéadú faoi \frac{6x-36}{x^{2}-36}.

$$3x\times \frac{6x-36}{x^{2}-36}+\frac{1}{6}x^{2}\times \frac{6x-36}{x^{2}-36}+12\times \frac{6x-36}{x^{2}-36}=x+12$$

Scríobh 3\times \frac{6x-36}{x^{2}-36} mar chodán aonair.

$$\frac{3\left(6x-36\right)}{x^{2}-36}x+\frac{1}{6}x^{2}\times \frac{6x-36}{x^{2}-36}+12\times \frac{6x-36}{x^{2}-36}=x+12$$

Méadaigh \frac{1}{6} faoi \frac{6x-36}{x^{2}-36} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$\frac{3\left(6x-36\right)}{x^{2}-36}x+\frac{6x-36}{6\left(x^{2}-36\right)}x^{2}+12\times \frac{6x-36}{x^{2}-36}=x+12$$

Scríobh 12\times \frac{6x-36}{x^{2}-36} mar chodán aonair.

$$\frac{3\left(6x-36\right)}{x^{2}-36}x+\frac{6x-36}{6\left(x^{2}-36\right)}x^{2}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Úsáid an t-airí dáileach chun 3 a mhéadú faoi 6x-36.

$$\frac{18x-108}{x^{2}-36}x+\frac{6x-36}{6\left(x^{2}-36\right)}x^{2}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Scríobh \frac{18x-108}{x^{2}-36}x mar chodán aonair.

$$\frac{\left(18x-108\right)x}{x^{2}-36}+\frac{6x-36}{6\left(x^{2}-36\right)}x^{2}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{6x-36}{6\left(x^{2}-36\right)}.

$$\frac{\left(18x-108\right)x}{x^{2}-36}+\frac{6\left(x-6\right)}{6\left(x-6\right)\left(x+6\right)}x^{2}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Cealaigh 6 mar uimhreoir agus ainmneoir.

$$\frac{\left(18x-108\right)x}{x^{2}-36}+\frac{x-6}{\left(x-6\right)\left(x+6\right)}x^{2}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Scríobh \frac{x-6}{\left(x-6\right)\left(x+6\right)}x^{2} mar chodán aonair.

$$\frac{\left(18x-108\right)x}{x^{2}-36}+\frac{\left(x-6\right)x^{2}}{\left(x-6\right)\left(x+6\right)}+\frac{12\left(6x-36\right)}{x^{2}-36}=x+12$$

Úsáid an t-airí dáileach chun 12 a mhéadú faoi 6x-36.

$$\frac{\left(18x-108\right)x}{x^{2}-36}+\frac{\left(x-6\right)x^{2}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{x^{2}-36}=x+12$$

Fachtóirigh x^{2}-36.

$$\frac{\left(18x-108\right)x}{\left(x-6\right)\left(x+6\right)}+\frac{\left(x-6\right)x^{2}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{x^{2}-36}=x+12$$

Tá an t-ainmneoir céanna ag \frac{\left(18x-108\right)x}{\left(x-6\right)\left(x+6\right)} agus \frac{\left(x-6\right)x^{2}}{\left(x-6\right)\left(x+6\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\left(18x-108\right)x+\left(x-6\right)x^{2}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{x^{2}-36}=x+12$$

Déan iolrúcháin in \left(18x-108\right)x+\left(x-6\right)x^{2}.

$$\frac{18x^{2}-108x+x^{3}-6x^{2}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{x^{2}-36}=x+12$$

Cumaisc téarmaí comhchosúla in: 18x^{2}-108x+x^{3}-6x^{2}.

$$\frac{12x^{2}-108x+x^{3}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{x^{2}-36}=x+12$$

Fachtóirigh x^{2}-36.

$$\frac{12x^{2}-108x+x^{3}}{\left(x-6\right)\left(x+6\right)}+\frac{72x-432}{\left(x-6\right)\left(x+6\right)}=x+12$$

Tá an t-ainmneoir céanna ag \frac{12x^{2}-108x+x^{3}}{\left(x-6\right)\left(x+6\right)} agus \frac{72x-432}{\left(x-6\right)\left(x+6\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{12x^{2}-108x+x^{3}+72x-432}{\left(x-6\right)\left(x+6\right)}=x+12$$

Cumaisc téarmaí comhchosúla in: 12x^{2}-108x+x^{3}+72x-432.

$$\frac{12x^{2}-36x+x^{3}-432}{\left(x-6\right)\left(x+6\right)}=x+12$$

Mar shampla \left(x-6\right)\left(x+6\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Cearnóg 6.

$$\frac{12x^{2}-36x+x^{3}-432}{x^{2}-36}=x+12$$

Bain x ón dá thaobh.

$$\frac{12x^{2}-36x+x^{3}-432}{x^{2}-36}-x=12$$

Fachtóirigh x^{2}-36.

$$\frac{12x^{2}-36x+x^{3}-432}{\left(x-6\right)\left(x+6\right)}-x=12$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh x faoi \frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}.

$$\frac{12x^{2}-36x+x^{3}-432}{\left(x-6\right)\left(x+6\right)}-\frac{x\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}=12$$

Tá an t-ainmneoir céanna ag \frac{12x^{2}-36x+x^{3}-432}{\left(x-6\right)\left(x+6\right)} agus \frac{x\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{12x^{2}-36x+x^{3}-432-x\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}=12$$

Déan iolrúcháin in 12x^{2}-36x+x^{3}-432-x\left(x-6\right)\left(x+6\right).

$$\frac{12x^{2}-36x+x^{3}-432-x^{3}-6x^{2}+6x^{2}+36x}{\left(x-6\right)\left(x+6\right)}=12$$

Cumaisc téarmaí comhchosúla in: 12x^{2}-36x+x^{3}-432-x^{3}-6x^{2}+6x^{2}+36x.

$$\frac{12x^{2}-432}{\left(x-6\right)\left(x+6\right)}=12$$

Bain 12 ón dá thaobh.

$$\frac{12x^{2}-432}{\left(x-6\right)\left(x+6\right)}-12=0$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 12 faoi \frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}.

$$\frac{12x^{2}-432}{\left(x-6\right)\left(x+6\right)}-\frac{12\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}=0$$

Tá an t-ainmneoir céanna ag \frac{12x^{2}-432}{\left(x-6\right)\left(x+6\right)} agus \frac{12\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{12x^{2}-432-12\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}=0$$

Déan iolrúcháin in 12x^{2}-432-12\left(x-6\right)\left(x+6\right).

$$\frac{12x^{2}-432-12x^{2}-72x+72x+432}{\left(x-6\right)\left(x+6\right)}=0$$

Cumaisc téarmaí comhchosúla in: 12x^{2}-432-12x^{2}-72x+72x+432.

$$\frac{0}{\left(x-6\right)\left(x+6\right)}=0$$

Ní féidir leis an athróg x a bheith comhionann le haon cheann de na luachanna -6,6 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi \left(x-6\right)\left(x+6\right).

$$0=0$$

Bíonn sé seo fíor i gcás x.

$$x\in \mathrm{R}$$

Ní féidir leis an athróg x a bheith comhionann le haon cheann de na luachanna -6,6,0.

$$x\in \mathrm{R}\setminus -6,0,6$$