Réitigh 5/x+1+6/x-1

$$\frac{ 5 }{ x+1 } + \frac{ 6 }{ x-1 }$$

Luacháil

$$\frac{11x+1}{x^{2}-1}$$

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 x-1 ná \left(x-1\right)\left(x+1\right). Méadaigh \frac{5}{x+1} faoi \frac{x-1}{x-1}. Méadaigh \frac{6}{x-1} faoi \frac{x+1}{x+1}.

$$\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} agus \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

Déan iolrúcháin in 5\left(x-1\right)+6\left(x+1\right).

$$\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)}$$

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

$$\frac{11x+1}{\left(x-1\right)\left(x+1\right)}$$

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

$$\frac{11x+1}{x^{2}-1}$$

Difreálaigh w.r.t. x

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

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 x-1 ná \left(x-1\right)\left(x+1\right). Méadaigh \frac{5}{x+1} faoi \frac{x-1}{x-1}. Méadaigh \frac{6}{x-1} faoi \frac{x+1}{x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

Tá an t-ainmneoir céanna ag \frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} agus \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

Déan iolrúcháin in 5\left(x-1\right)+6\left(x+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{\left(x-1\right)\left(x+1\right)})$$

Mar shampla \left(x-1\right)\left(x+1\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1^{2}})$$

Ríomh cumhacht 1 de 2 agus faigh 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1})$$

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.

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

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}.

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

Déan an uimhríocht.

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

Fairsingigh ag baint úsáid as an airí dáileach.

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

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

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

Déan an uimhríocht.

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

Bain lúibíní ar bith nach bhfuil gá leo.

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

Cuir téarmaí cosúla le chéile.

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

Dealaigh 22 ó 11.

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

Do théarma ar bith t, t^{1}=t.

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

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

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