Réitigh 2/x+2-7/x-3

$$\frac{ 2 }{ x+2 } - \frac{ 7 }{ x-3 }$$

Luacháil

$$-\frac{5\left(x+4\right)}{\left(x-3\right)\left(x+2\right)}$$

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+2 agus x-3 ná \left(x-3\right)\left(x+2\right). Méadaigh \frac{2}{x+2} faoi \frac{x-3}{x-3}. Méadaigh \frac{7}{x-3} faoi \frac{x+2}{x+2}.

$$\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}-\frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}$$

Tá an t-ainmneoir céanna ag \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} agus \frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{2\left(x-3\right)-7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}$$

Déan iolrúcháin in 2\left(x-3\right)-7\left(x+2\right).

$$\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)}$$

Cumaisc téarmaí comhchosúla in: 2x-6-7x-14.

$$\frac{-5x-20}{\left(x-3\right)\left(x+2\right)}$$

Fairsingigh \left(x-3\right)\left(x+2\right)

$$\frac{-5x-20}{x^{2}-x-6}$$

Difreálaigh w.r.t. x

$$\frac{5\left(\left(x+4\right)^{2}-14\right)}{\left(\left(x-3\right)\left(x+2\right)\right)^{2}}$$

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+2 agus x-3 ná \left(x-3\right)\left(x+2\right). Méadaigh \frac{2}{x+2} faoi \frac{x-3}{x-3}. Méadaigh \frac{7}{x-3} faoi \frac{x+2}{x+2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}-\frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)})$$

Tá an t-ainmneoir céanna ag \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} agus \frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-3\right)-7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)})$$

Déan iolrúcháin in 2\left(x-3\right)-7\left(x+2\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)})$$

Cumaisc téarmaí comhchosúla in: 2x-6-7x-14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{\left(x-3\right)\left(x+2\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-3 a iolrú faoi gach téarma de x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}+2x-3x-6})$$

Comhcheangail 2x agus -3x chun -x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}-x-6})$$

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.

$$\frac{\left(x^{2}-x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}-20)-\left(-5x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-6)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{1-1}-\left(-5x^{1}-20\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Méadaigh x^{2}-x^{1}-6 faoi -5x^{0}.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Méadaigh -5x^{1}-20 faoi 2x^{1}-x^{0}.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}\times 2x^{1}-5x^{1}\left(-1\right)x^{0}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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

$$\frac{-5x^{2}-\left(-5x^{1}\right)-6\left(-5\right)x^{0}-\left(-5\times 2x^{1+1}-5\left(-1\right)x^{1}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Simpligh.

$$\frac{-5x^{2}+5x^{1}+30x^{0}-\left(-10x^{2}+5x^{1}-40x^{1}+20x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{5x^{2}+40x^{1}+10x^{0}}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{5x^{2}+40x+10x^{0}}{\left(x^{2}-x-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10\times 1}{\left(x^{2}-x-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10}{\left(x^{2}-x-6\right)^{2}}$$