Réitigh 1/2x-1+1/2x+1+x/4x^2-1

$$\frac { 1 } { 2 x - 1 } + \frac { 1 } { 2 x + 1 } + \frac { x } { 4 x ^ { 2 } - 1 }$$

Luacháil

$$\frac{5x}{4x^{2}-1}$$

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 2x-1 agus 2x+1 ná \left(2x-1\right)\left(2x+1\right). Méadaigh \frac{1}{2x-1} faoi \frac{2x+1}{2x+1}. Méadaigh \frac{1}{2x+1} faoi \frac{2x-1}{2x-1}.

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

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

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

Cumaisc téarmaí comhchosúla in: 2x+1+2x-1.

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

Fachtóirigh 4x^{2}-1.

$$\frac{4x}{\left(2x-1\right)\left(2x+1\right)}+\frac{x}{\left(2x-1\right)\left(2x+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{4x}{\left(2x-1\right)\left(2x+1\right)} agus \frac{x}{\left(2x-1\right)\left(2x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4x+x}{\left(2x-1\right)\left(2x+1\right)}$$

Cumaisc téarmaí comhchosúla in: 4x+x.

$$\frac{5x}{\left(2x-1\right)\left(2x+1\right)}$$

Fairsingigh \left(2x-1\right)\left(2x+1\right)

$$\frac{5x}{4x^{2}-1}$$

Difreálaigh w.r.t. x

$$-\frac{5\left(4x^{2}+1\right)}{\left(4x^{2}-1\right)^{2}}$$

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 2x-1 agus 2x+1 ná \left(2x-1\right)\left(2x+1\right). Méadaigh \frac{1}{2x-1} faoi \frac{2x+1}{2x+1}. Méadaigh \frac{1}{2x+1} faoi \frac{2x-1}{2x-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+1}{\left(2x-1\right)\left(2x+1\right)}+\frac{2x-1}{\left(2x-1\right)\left(2x+1\right)}+\frac{x}{4x^{2}-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+1+2x-1}{\left(2x-1\right)\left(2x+1\right)}+\frac{x}{4x^{2}-1})$$

Cumaisc téarmaí comhchosúla in: 2x+1+2x-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{\left(2x-1\right)\left(2x+1\right)}+\frac{x}{4x^{2}-1})$$

Fachtóirigh 4x^{2}-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{\left(2x-1\right)\left(2x+1\right)}+\frac{x}{\left(2x-1\right)\left(2x+1\right)})$$

Tá an t-ainmneoir céanna ag \frac{4x}{\left(2x-1\right)\left(2x+1\right)} agus \frac{x}{\left(2x-1\right)\left(2x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+x}{\left(2x-1\right)\left(2x+1\right)})$$

Cumaisc téarmaí comhchosúla in: 4x+x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{\left(2x-1\right)\left(2x+1\right)})$$

Mar shampla \left(2x-1\right)\left(2x+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}. Cearnóg 1.

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

Fairsingigh \left(2x\right)^{2}

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{2^{2}x^{2}-1})$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{4x^{2}-1})$$

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.

$$\frac{\left(4x^{2}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})-5x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}-1)}{\left(4x^{2}-1\right)^{2}}$$

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}.

$$\frac{\left(4x^{2}-1\right)\times 5x^{1-1}-5x^{1}\times 2\times 4x^{2-1}}{\left(4x^{2}-1\right)^{2}}$$

Déan an uimhríocht.

$$\frac{\left(4x^{2}-1\right)\times 5x^{0}-5x^{1}\times 8x^{1}}{\left(4x^{2}-1\right)^{2}}$$

Fairsingigh ag baint úsáid as an airí dáileach.

$$\frac{4x^{2}\times 5x^{0}-5x^{0}-5x^{1}\times 8x^{1}}{\left(4x^{2}-1\right)^{2}}$$

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

$$\frac{4\times 5x^{2}-5x^{0}-5\times 8x^{1+1}}{\left(4x^{2}-1\right)^{2}}$$

Déan an uimhríocht.

$$\frac{20x^{2}-5x^{0}-40x^{2}}{\left(4x^{2}-1\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{\left(20-40\right)x^{2}-5x^{0}}{\left(4x^{2}-1\right)^{2}}$$

Dealaigh 40 ó 20.

$$\frac{-20x^{2}-5x^{0}}{\left(4x^{2}-1\right)^{2}}$$

Fág 5 as an áireamh.

$$\frac{5\left(-4x^{2}-x^{0}\right)}{\left(4x^{2}-1\right)^{2}}$$

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

$$\frac{5\left(-4x^{2}-1\right)}{\left(4x^{2}-1\right)^{2}}$$