Réitigh 4/x-7+3/x+2

$$\frac { 4 } { x - 7 } + \frac { 3 } { x + 2 }$$

Luacháil

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

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-7 agus x+2 ná \left(x-7\right)\left(x+2\right). Méadaigh \frac{4}{x-7} faoi \frac{x+2}{x+2}. Méadaigh \frac{3}{x+2} faoi \frac{x-7}{x-7}.

$$\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

Tá an t-ainmneoir céanna ag \frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} agus \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

Déan iolrúcháin in 4\left(x+2\right)+3\left(x-7\right).

$$\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)}$$

Cumaisc téarmaí comhchosúla in: 4x+8+3x-21.

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

Fairsingigh \left(x-7\right)\left(x+2\right)

$$\frac{7x-13}{x^{2}-5x-14}$$

Difreálaigh w.r.t. x

$$\frac{-7x^{2}+26x-163}{\left(\left(x-7\right)\left(x+2\right)\right)^{2}}$$

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-7 agus x+2 ná \left(x-7\right)\left(x+2\right). Méadaigh \frac{4}{x-7} faoi \frac{x+2}{x+2}. Méadaigh \frac{3}{x+2} faoi \frac{x-7}{x-7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

Tá an t-ainmneoir céanna ag \frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} agus \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

Déan iolrúcháin in 4\left(x+2\right)+3\left(x-7\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)})$$

Cumaisc téarmaí comhchosúla in: 4x+8+3x-21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{\left(x-7\right)\left(x+2\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-7 a iolrú faoi gach téarma de x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}+2x-7x-14})$$

Comhcheangail 2x agus -7x chun -5x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}-5x-14})$$

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.

$$\frac{\left(x^{2}-5x^{1}-14\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-13)-\left(7x^{1}-13\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x^{1}-14)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{1-1}-\left(7x^{1}-13\right)\left(2x^{2-1}-5x^{1-1}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Méadaigh x^{2}-5x^{1}-14 faoi 7x^{0}.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Méadaigh 7x^{1}-13 faoi 2x^{1}-5x^{0}.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}\times 2x^{1}+7x^{1}\left(-5\right)x^{0}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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

$$\frac{7x^{2}-5\times 7x^{1}-14\times 7x^{0}-\left(7\times 2x^{1+1}+7\left(-5\right)x^{1}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Simpligh.

$$\frac{7x^{2}-35x^{1}-98x^{0}-\left(14x^{2}-35x^{1}-26x^{1}+65x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{-7x^{2}+26x^{1}-163x^{0}}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{-7x^{2}+26x-163x^{0}}{\left(x^{2}-5x-14\right)^{2}}$$

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

$$\frac{-7x^{2}+26x-163}{\left(x^{2}-5x-14\right)^{2}}$$