Réitigh 5/x-1-4/4x

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

Luacháil

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

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

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

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

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

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

$$\frac{20x-4x+4}{4x\left(x-1\right)}$$

Cumaisc téarmaí comhchosúla in: 20x-4x+4.

$$\frac{16x+4}{4x\left(x-1\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{16x+4}{4x\left(x-1\right)}.

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

Cealaigh 4 mar uimhreoir agus ainmneoir.

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

Fairsingigh x\left(x-1\right)

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

Difreálaigh w.r.t. x

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

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20x-4x+4}{4x\left(x-1\right)})$$

Cumaisc téarmaí comhchosúla in: 20x-4x+4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x+4}{4x\left(x-1\right)})$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{16x+4}{4x\left(x-1\right)}.

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

Cealaigh 4 mar uimhreoir agus ainmneoir.

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

Úsáid an t-airí dáileach chun x a mhéadú faoi x-1.

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

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.

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

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}.

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

Simpligh.

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

Méadaigh x^{2}-x^{1} faoi 4x^{0}.

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

Méadaigh 4x^{1}+1 faoi 2x^{1}-x^{0}.

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

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

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

Simpligh.

$$\frac{4x^{2}-4x^{1}-\left(8x^{2}-4x^{1}+2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

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

Do théarma ar bith t, t^{1}=t.

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

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

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