Réitigh 6/x-4+5/x+3

$$\frac { 6 } { x - 4 } + \frac { 5 } { x + 3 }$$

Luacháil

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

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-4 agus x+3 ná \left(x-4\right)\left(x+3\right). Méadaigh \frac{6}{x-4} faoi \frac{x+3}{x+3}. Méadaigh \frac{5}{x+3} faoi \frac{x-4}{x-4}.

$$\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

Tá an t-ainmneoir céanna ag \frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} agus \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

Déan iolrúcháin in 6\left(x+3\right)+5\left(x-4\right).

$$\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)}$$

Cumaisc téarmaí comhchosúla in: 6x+18+5x-20.

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

Fairsingigh \left(x-4\right)\left(x+3\right)

$$\frac{11x-2}{x^{2}-x-12}$$

Difreálaigh w.r.t. x

$$\frac{-11x^{2}+4x-134}{\left(\left(x-4\right)\left(x+3\right)\right)^{2}}$$

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-4 agus x+3 ná \left(x-4\right)\left(x+3\right). Méadaigh \frac{6}{x-4} faoi \frac{x+3}{x+3}. Méadaigh \frac{5}{x+3} faoi \frac{x-4}{x-4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

Tá an t-ainmneoir céanna ag \frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} agus \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

Déan iolrúcháin in 6\left(x+3\right)+5\left(x-4\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)})$$

Cumaisc téarmaí comhchosúla in: 6x+18+5x-20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{\left(x-4\right)\left(x+3\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-4 a iolrú faoi gach téarma de x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}+3x-4x-12})$$

Comhcheangail 3x agus -4x chun -x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}-x-12})$$

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.

$$\frac{\left(x^{2}-x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(11x^{1}-2)-\left(11x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-12)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{1-1}-\left(11x^{1}-2\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Méadaigh x^{2}-x^{1}-12 faoi 11x^{0}.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Méadaigh 11x^{1}-2 faoi 2x^{1}-x^{0}.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}\times 2x^{1}+11x^{1}\left(-1\right)x^{0}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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

$$\frac{11x^{2}-11x^{1}-12\times 11x^{0}-\left(11\times 2x^{1+1}+11\left(-1\right)x^{1}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{11x^{2}-11x^{1}-132x^{0}-\left(22x^{2}-11x^{1}-4x^{1}+2x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{-11x^{2}+4x^{1}-134x^{0}}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{-11x^{2}+4x-134x^{0}}{\left(x^{2}-x-12\right)^{2}}$$

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

$$\frac{-11x^{2}+4x-134}{\left(x^{2}-x-12\right)^{2}}$$