Réitigh 3/x-6+4/x+4

$$\frac { 3 } { x - 6 } + \frac { 4 } { x + 4 }$$

Luacháil

$$\frac{7x-12}{\left(x-6\right)\left(x+4\right)}$$

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-6 agus x+4 ná \left(x-6\right)\left(x+4\right). Méadaigh \frac{3}{x-6} faoi \frac{x+4}{x+4}. Méadaigh \frac{4}{x+4} faoi \frac{x-6}{x-6}.

$$\frac{3\left(x+4\right)}{\left(x-6\right)\left(x+4\right)}+\frac{4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)}$$

Tá an t-ainmneoir céanna ag \frac{3\left(x+4\right)}{\left(x-6\right)\left(x+4\right)} agus \frac{4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{3\left(x+4\right)+4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)}$$

Déan iolrúcháin in 3\left(x+4\right)+4\left(x-6\right).

$$\frac{3x+12+4x-24}{\left(x-6\right)\left(x+4\right)}$$

Cumaisc téarmaí comhchosúla in: 3x+12+4x-24.

$$\frac{7x-12}{\left(x-6\right)\left(x+4\right)}$$

Fairsingigh \left(x-6\right)\left(x+4\right)

$$\frac{7x-12}{x^{2}-2x-24}$$

Difreálaigh w.r.t. x

$$\frac{-7x^{2}+24x-192}{\left(\left(x-6\right)\left(x+4\right)\right)^{2}}$$

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-6 agus x+4 ná \left(x-6\right)\left(x+4\right). Méadaigh \frac{3}{x-6} faoi \frac{x+4}{x+4}. Méadaigh \frac{4}{x+4} faoi \frac{x-6}{x-6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+4\right)}{\left(x-6\right)\left(x+4\right)}+\frac{4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)})$$

Tá an t-ainmneoir céanna ag \frac{3\left(x+4\right)}{\left(x-6\right)\left(x+4\right)} agus \frac{4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+4\right)+4\left(x-6\right)}{\left(x-6\right)\left(x+4\right)})$$

Déan iolrúcháin in 3\left(x+4\right)+4\left(x-6\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+12+4x-24}{\left(x-6\right)\left(x+4\right)})$$

Cumaisc téarmaí comhchosúla in: 3x+12+4x-24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-12}{\left(x-6\right)\left(x+4\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-6 a iolrú faoi gach téarma de x+4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-12}{x^{2}+4x-6x-24})$$

Comhcheangail 4x agus -6x chun -2x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-12}{x^{2}-2x-24})$$

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.

$$\frac{\left(x^{2}-2x^{1}-24\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-12)-\left(7x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}-24)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-2x^{1}-24\right)\times 7x^{1-1}-\left(7x^{1}-12\right)\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-2x^{1}-24\right)\times 7x^{0}-\left(7x^{1}-12\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Méadaigh x^{2}-2x^{1}-24 faoi 7x^{0}.

$$\frac{x^{2}\times 7x^{0}-2x^{1}\times 7x^{0}-24\times 7x^{0}-\left(7x^{1}-12\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Méadaigh 7x^{1}-12 faoi 2x^{1}-2x^{0}.

$$\frac{x^{2}\times 7x^{0}-2x^{1}\times 7x^{0}-24\times 7x^{0}-\left(7x^{1}\times 2x^{1}+7x^{1}\left(-2\right)x^{0}-12\times 2x^{1}-12\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

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

$$\frac{7x^{2}-2\times 7x^{1}-24\times 7x^{0}-\left(7\times 2x^{1+1}+7\left(-2\right)x^{1}-12\times 2x^{1}-12\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Simpligh.

$$\frac{7x^{2}-14x^{1}-168x^{0}-\left(14x^{2}-14x^{1}-24x^{1}+24x^{0}\right)}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{-7x^{2}+24x^{1}-192x^{0}}{\left(x^{2}-2x^{1}-24\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{-7x^{2}+24x-192x^{0}}{\left(x^{2}-2x-24\right)^{2}}$$

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

$$\frac{-7x^{2}+24x-192}{\left(x^{2}-2x-24\right)^{2}}$$