Réitigh 4*6/x^2-4x+3-3/3-x-4/x-1

$$\frac { 4 \times 6 } { x ^ { 2 } - 4 x + 3 } - \frac { 3 } { 3 - x } - \frac { 4 } { x - 1 }$$

Luacháil

$$\frac{x-33}{\left(3-x\right)\left(x-1\right)}$$

Céimeanna gearra réitigh

Méadaigh 4 agus 6 chun 24 a fháil.

$$\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1}$$

Fachtóirigh x^{2}-4x+3.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1}$$

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-3\right)\left(x-1\right) agus 3-x ná \left(x-3\right)\left(x-1\right). Méadaigh \frac{3}{3-x} faoi \frac{-\left(x-1\right)}{-\left(x-1\right)}.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Tá an t-ainmneoir céanna ag \frac{24}{\left(x-3\right)\left(x-1\right)} agus \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Déan iolrúcháin in 24-3\left(-1\right)\left(x-1\right).

$$\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Cumaisc téarmaí comhchosúla in: 24+3x-3.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

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-3\right)\left(x-1\right) agus x-1 ná \left(x-3\right)\left(x-1\right). Méadaigh \frac{4}{x-1} faoi \frac{x-3}{x-3}.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Tá an t-ainmneoir céanna ag \frac{21+3x}{\left(x-3\right)\left(x-1\right)} agus \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Déan iolrúcháin in 21+3x-4\left(x-3\right).

$$\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)}$$

Cumaisc téarmaí comhchosúla in: 21+3x-4x+12.

$$\frac{33-x}{\left(x-3\right)\left(x-1\right)}$$

Fairsingigh \left(x-3\right)\left(x-1\right)

$$\frac{33-x}{x^{2}-4x+3}$$

Difreálaigh w.r.t. x

$$\frac{x^{2}-66x+129}{x^{4}-8x^{3}+22x^{2}-24x+9}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Méadaigh 4 agus 6 chun 24 a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1})$$

Fachtóirigh x^{2}-4x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1})$$

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-3\right)\left(x-1\right) agus 3-x ná \left(x-3\right)\left(x-1\right). Méadaigh \frac{3}{3-x} faoi \frac{-\left(x-1\right)}{-\left(x-1\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Tá an t-ainmneoir céanna ag \frac{24}{\left(x-3\right)\left(x-1\right)} agus \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Déan iolrúcháin in 24-3\left(-1\right)\left(x-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Cumaisc téarmaí comhchosúla in: 24+3x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

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-3\right)\left(x-1\right) agus x-1 ná \left(x-3\right)\left(x-1\right). Méadaigh \frac{4}{x-1} faoi \frac{x-3}{x-3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Tá an t-ainmneoir céanna ag \frac{21+3x}{\left(x-3\right)\left(x-1\right)} agus \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Déan iolrúcháin in 21+3x-4\left(x-3\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)})$$

Cumaisc téarmaí comhchosúla in: 21+3x-4x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{\left(x-3\right)\left(x-1\right)})$$

Úsáid an t-airí dáileach chun x-3 a mhéadú faoi x-1 agus chun téarmaí comhchosúla a chumasc.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{x^{2}-4x+3})$$

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.

$$\frac{\left(x^{2}-4x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+33)-\left(-x^{1}+33\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}+3)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{1-1}-\left(-x^{1}+33\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Méadaigh x^{2}-4x^{1}+3 faoi -x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Méadaigh -x^{1}+33 faoi 2x^{1}-4x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-4\right)x^{0}+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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

$$\frac{-x^{2}-4\left(-1\right)x^{1}+3\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-4x^{1}\right)+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Simpligh.

$$\frac{-x^{2}+4x^{1}-3x^{0}-\left(-2x^{2}+4x^{1}+66x^{1}-132x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{x^{2}-66x^{1}+129x^{0}}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{x^{2}-66x+129x^{0}}{\left(x^{2}-4x+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129\times 1}{\left(x^{2}-4x+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129}{\left(x^{2}-4x+3\right)^{2}}$$