Réitigh x/x^2-100+2/10-x

$$\frac { x } { x ^ { 2 } - 100 } + \frac { 2 } { 10 - x }$$

Luacháil

$$\frac{x+20}{100-x^{2}}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}-100.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x}$$

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-10\right)\left(x+10\right) agus 10-x ná \left(x-10\right)\left(x+10\right). Méadaigh \frac{2}{10-x} faoi \frac{-\left(x+10\right)}{-\left(x+10\right)}.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

Tá an t-ainmneoir céanna ag \frac{x}{\left(x-10\right)\left(x+10\right)} agus \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

Déan iolrúcháin in x+2\left(-1\right)\left(x+10\right).

$$\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)}$$

Cumaisc téarmaí comhchosúla in: x-2x-20.

$$\frac{-x-20}{\left(x-10\right)\left(x+10\right)}$$

Fairsingigh \left(x-10\right)\left(x+10\right)

$$\frac{-x-20}{x^{2}-100}$$

Difreálaigh w.r.t. x

$$\frac{x^{2}+40x+100}{\left(100-x^{2}\right)^{2}}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Fachtóirigh x^{2}-100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x})$$

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-10\right)\left(x+10\right) agus 10-x ná \left(x-10\right)\left(x+10\right). Méadaigh \frac{2}{10-x} faoi \frac{-\left(x+10\right)}{-\left(x+10\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

Tá an t-ainmneoir céanna ag \frac{x}{\left(x-10\right)\left(x+10\right)} agus \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

Déan iolrúcháin in x+2\left(-1\right)\left(x+10\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)})$$

Cumaisc téarmaí comhchosúla in: x-2x-20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{\left(x-10\right)\left(x+10\right)})$$

Mar shampla \left(x-10\right)\left(x+10\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}. Cearnóg 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{x^{2}-100})$$

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.

$$\frac{\left(x^{2}-100\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}-20)-\left(-x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-100)}{\left(x^{2}-100\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{1-1}-\left(-x^{1}-20\right)\times 2x^{2-1}}{\left(x^{2}-100\right)^{2}}$$

Déan an uimhríocht.

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{0}-\left(-x^{1}-20\right)\times 2x^{1}}{\left(x^{2}-100\right)^{2}}$$

Fairsingigh ag baint úsáid as an airí dáileach.

$$\frac{x^{2}\left(-1\right)x^{0}-100\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{-x^{2}-100\left(-1\right)x^{0}-\left(-2x^{1+1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Déan an uimhríocht.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Bain lúibíní ar bith nach bhfuil gá leo.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}\right)-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{\left(-1-\left(-2\right)\right)x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Dealaigh -2 ó -1.

$$\frac{x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{x^{2}+100x^{0}-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100\times 1-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$