Réitigh 3/x-6-2/x+2

$$\frac { 3 } { x - 6 } - \frac { 2 } { x + 2 }$$

Luacháil

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x-6 agus x+2 ná \left(x-6\right)\left(x+2\right). Méadaigh \frac{3}{x-6} faoi \frac{x+2}{x+2}. Méadaigh \frac{2}{x+2} faoi \frac{x-6}{x-6}.

$$\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}-\frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}$$

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

$$\frac{3\left(x+2\right)-2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}$$

Déan iolrúcháin in 3\left(x+2\right)-2\left(x-6\right).

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

Cumaisc téarmaí comhchosúla in: 3x+6-2x+12.

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

Fairsingigh \left(x-6\right)\left(x+2\right)

$$\frac{x+18}{x^{2}-4x-12}$$

Difreálaigh w.r.t. x

$$\frac{60-36x-x^{2}}{x^{4}-8x^{3}-8x^{2}+96x+144}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x-6 agus x+2 ná \left(x-6\right)\left(x+2\right). Méadaigh \frac{3}{x-6} faoi \frac{x+2}{x+2}. Méadaigh \frac{2}{x+2} faoi \frac{x-6}{x-6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}-\frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+2\right)-2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)})$$

Déan iolrúcháin in 3\left(x+2\right)-2\left(x-6\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+6-2x+12}{\left(x-6\right)\left(x+2\right)})$$

Cumaisc téarmaí comhchosúla in: 3x+6-2x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{\left(x-6\right)\left(x+2\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-6 a iolrú faoi gach téarma de x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}+2x-6x-12})$$

Comhcheangail 2x agus -6x chun -4x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}-4x-12})$$

Do dhá fheidhm indifreáilte ar bith, is ionann díorthach líon an dá fheidhme agus an t-ainmneoir méadaithe faoi dhíorthach an uimhreora lúide an t-uimhreoir méadaithe faoi dhíorthach an ainmneora, agus iad ar fad roinnte faoin ainmneoir cearnaithe.

$$\frac{\left(x^{2}-4x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+18)-\left(x^{1}+18\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}-12)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{1-1}-\left(x^{1}+18\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Méadaigh x^{2}-4x^{1}-12 faoi x^{0}.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Méadaigh x^{1}+18 faoi 2x^{1}-4x^{0}.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-4\right)x^{0}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Chun cumhachtaí an bhoinn chéanna a mhéadú, suimigh a n-easpónaint.

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{1+1}-4x^{1}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{2}-4x^{1}+36x^{1}-72x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{-x^{2}-36x^{1}+60x^{0}}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{-x^{2}-36x+60x^{0}}{\left(x^{2}-4x-12\right)^{2}}$$

Do théarma ar bith t ach amháin 0, t^{0}=1.

$$\frac{-x^{2}-36x+60\times 1}{\left(x^{2}-4x-12\right)^{2}}$$

Do théarma ar bith t, t\times 1=t agus 1t=t.

$$\frac{-x^{2}-36x+60}{\left(x^{2}-4x-12\right)^{2}}$$