Réitigh 3/1+x-2x^2+x/x-1

$$\frac{ 3 }{ 1+x-2 { x }^{ 2 } } + \frac{ x }{ x-1 }$$

Luacháil

$$\frac{2x+3}{2x+1}$$

Céimeanna gearra réitigh

Fachtóirigh 1+x-2x^{2}.

$$\frac{3}{\left(-x+1\right)\left(2x+1\right)}+\frac{x}{x-1}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(-x+1\right)\left(2x+1\right) agus x-1 ná \left(x-1\right)\left(2x+1\right). Méadaigh \frac{3}{\left(-x+1\right)\left(2x+1\right)} faoi \frac{-1}{-1}. Méadaigh \frac{x}{x-1} faoi \frac{2x+1}{2x+1}.

$$\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)}+\frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} agus \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{3\left(-1\right)+x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)}$$

Déan iolrúcháin in 3\left(-1\right)+x\left(2x+1\right).

$$\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}.

$$\frac{\left(x-1\right)\left(2x+3\right)}{\left(x-1\right)\left(2x+1\right)}$$

Cealaigh x-1 mar uimhreoir agus ainmneoir.

$$\frac{2x+3}{2x+1}$$

Difreálaigh w.r.t. x

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

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Fachtóirigh 1+x-2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{\left(-x+1\right)\left(2x+1\right)}+\frac{x}{x-1})$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(-x+1\right)\left(2x+1\right) agus x-1 ná \left(x-1\right)\left(2x+1\right). Méadaigh \frac{3}{\left(-x+1\right)\left(2x+1\right)} faoi \frac{-1}{-1}. Méadaigh \frac{x}{x-1} faoi \frac{2x+1}{2x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)}+\frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)})$$

Tá an t-ainmneoir céanna ag \frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} agus \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(-1\right)+x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)})$$

Déan iolrúcháin in 3\left(-1\right)+x\left(2x+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)})$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-1\right)\left(2x+3\right)}{\left(x-1\right)\left(2x+1\right)})$$

Cealaigh x-1 mar uimhreoir agus ainmneoir.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+3}{2x+1})$$

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.

$$\frac{\left(2x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+3)-\left(2x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+1)}{\left(2x^{1}+1\right)^{2}}$$

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}.

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

Déan an uimhríocht.

$$\frac{\left(2x^{1}+1\right)\times 2x^{0}-\left(2x^{1}+3\right)\times 2x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Fairsingigh ag baint úsáid as an airí dáileach.

$$\frac{2x^{1}\times 2x^{0}+2x^{0}-\left(2x^{1}\times 2x^{0}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

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

$$\frac{2\times 2x^{1}+2x^{0}-\left(2\times 2x^{1}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

Déan an uimhríocht.

$$\frac{4x^{1}+2x^{0}-\left(4x^{1}+6x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

Bain lúibíní ar bith nach bhfuil gá leo.

$$\frac{4x^{1}+2x^{0}-4x^{1}-6x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{\left(4-4\right)x^{1}+\left(2-6\right)x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Dealaigh 4 ó 4 agus 6 ó 2.

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

Do théarma ar bith t, t^{1}=t.

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

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

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