Réitigh 4/x-2-5/x+1

$$\frac{4}{x-2} - \frac{5}{x+1}$$

Luacháil

$$\frac{14-x}{\left(x-2\right)\left(x+1\right)}$$

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+1 ná \left(x-2\right)\left(x+1\right). Méadaigh \frac{4}{x-2} faoi \frac{x+1}{x+1}. Méadaigh \frac{5}{x+1} faoi \frac{x-2}{x-2}.

$$\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} agus \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

Déan iolrúcháin in 4\left(x+1\right)-5\left(x-2\right).

$$\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)}$$

Cumaisc téarmaí comhchosúla in: 4x+4-5x+10.

$$\frac{-x+14}{\left(x-2\right)\left(x+1\right)}$$

Fairsingigh \left(x-2\right)\left(x+1\right)

$$\frac{-x+14}{x^{2}-x-2}$$

Difreálaigh w.r.t. x

$$\frac{x^{2}-28x+16}{x^{4}-2x^{3}-3x^{2}+4x+4}$$

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+1 ná \left(x-2\right)\left(x+1\right). Méadaigh \frac{4}{x-2} faoi \frac{x+1}{x+1}. Méadaigh \frac{5}{x+1} faoi \frac{x-2}{x-2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

Tá an t-ainmneoir céanna ag \frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} agus \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

Déan iolrúcháin in 4\left(x+1\right)-5\left(x-2\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)})$$

Cumaisc téarmaí comhchosúla in: 4x+4-5x+10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{\left(x-2\right)\left(x+1\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-2 a iolrú faoi gach téarma de x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{x^{2}+x-2x-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{x^{2}-x-2})$$

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.

$$\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+14)-\left(-x^{1}+14\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-2\right)\left(-1\right)x^{1-1}-\left(-x^{1}+14\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-x^{1}-2\right)\left(-1\right)x^{0}-\left(-x^{1}+14\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Méadaigh x^{2}-x^{1}-2 faoi -x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-x^{1}\left(-1\right)x^{0}-2\left(-1\right)x^{0}-\left(-x^{1}+14\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Méadaigh -x^{1}+14 faoi 2x^{1}-x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-x^{1}\left(-1\right)x^{0}-2\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-1\right)x^{0}+14\times 2x^{1}+14\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{-x^{2}-\left(-x^{1}\right)-2\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-x^{1}\right)+14\times 2x^{1}+14\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Simpligh.

$$\frac{-x^{2}+x^{1}+2x^{0}-\left(-2x^{2}+x^{1}+28x^{1}-14x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{x^{2}-28x^{1}+16x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{x^{2}-28x+16x^{0}}{\left(x^{2}-x-2\right)^{2}}$$

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

$$\frac{x^{2}-28x+16\times 1}{\left(x^{2}-x-2\right)^{2}}$$

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

$$\frac{x^{2}-28x+16}{\left(x^{2}-x-2\right)^{2}}$$