Réitigh 3/2x+1-5/x-2

$$\frac { 3 } { 2 x + 1 } - \frac { 5 } { x - 2 }$$

Luacháil

$$-\frac{7x+11}{\left(x-2\right)\left(2x+1\right)}$$

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 2x+1 agus x-2 ná \left(x-2\right)\left(2x+1\right). Méadaigh \frac{3}{2x+1} faoi \frac{x-2}{x-2}. Méadaigh \frac{5}{x-2} faoi \frac{2x+1}{2x+1}.

$$\frac{3\left(x-2\right)}{\left(x-2\right)\left(2x+1\right)}-\frac{5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{3\left(x-2\right)}{\left(x-2\right)\left(2x+1\right)} agus \frac{5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{3\left(x-2\right)-5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)}$$

Déan iolrúcháin in 3\left(x-2\right)-5\left(2x+1\right).

$$\frac{3x-6-10x-5}{\left(x-2\right)\left(2x+1\right)}$$

Cumaisc téarmaí comhchosúla in: 3x-6-10x-5.

$$\frac{-7x-11}{\left(x-2\right)\left(2x+1\right)}$$

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

$$\frac{-7x-11}{2x^{2}-3x-2}$$

Difreálaigh w.r.t. x

$$\frac{14x^{2}+44x-19}{4x^{4}-12x^{3}+x^{2}+12x+4}$$

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 x-2 ná \left(x-2\right)\left(2x+1\right). Méadaigh \frac{3}{2x+1} faoi \frac{x-2}{x-2}. Méadaigh \frac{5}{x-2} faoi \frac{2x+1}{2x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-2\right)}{\left(x-2\right)\left(2x+1\right)}-\frac{5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)})$$

Tá an t-ainmneoir céanna ag \frac{3\left(x-2\right)}{\left(x-2\right)\left(2x+1\right)} agus \frac{5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-2\right)-5\left(2x+1\right)}{\left(x-2\right)\left(2x+1\right)})$$

Déan iolrúcháin in 3\left(x-2\right)-5\left(2x+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-6-10x-5}{\left(x-2\right)\left(2x+1\right)})$$

Cumaisc téarmaí comhchosúla in: 3x-6-10x-5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-7x-11}{\left(x-2\right)\left(2x+1\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-2 a iolrú faoi gach téarma de 2x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-7x-11}{2x^{2}+x-4x-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-7x-11}{2x^{2}-3x-2})$$

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.

$$\frac{\left(2x^{2}-3x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{1}-11)-\left(-7x^{1}-11\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-3x^{1}-2)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

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}.

$$\frac{\left(2x^{2}-3x^{1}-2\right)\left(-7\right)x^{1-1}-\left(-7x^{1}-11\right)\left(2\times 2x^{2-1}-3x^{1-1}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Simpligh.

$$\frac{\left(2x^{2}-3x^{1}-2\right)\left(-7\right)x^{0}-\left(-7x^{1}-11\right)\left(4x^{1}-3x^{0}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Méadaigh 2x^{2}-3x^{1}-2 faoi -7x^{0}.

$$\frac{2x^{2}\left(-7\right)x^{0}-3x^{1}\left(-7\right)x^{0}-2\left(-7\right)x^{0}-\left(-7x^{1}-11\right)\left(4x^{1}-3x^{0}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Méadaigh -7x^{1}-11 faoi 4x^{1}-3x^{0}.

$$\frac{2x^{2}\left(-7\right)x^{0}-3x^{1}\left(-7\right)x^{0}-2\left(-7\right)x^{0}-\left(-7x^{1}\times 4x^{1}-7x^{1}\left(-3\right)x^{0}-11\times 4x^{1}-11\left(-3\right)x^{0}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

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

$$\frac{2\left(-7\right)x^{2}-3\left(-7\right)x^{1}-2\left(-7\right)x^{0}-\left(-7\times 4x^{1+1}-7\left(-3\right)x^{1}-11\times 4x^{1}-11\left(-3\right)x^{0}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Simpligh.

$$\frac{-14x^{2}+21x^{1}+14x^{0}-\left(-28x^{2}+21x^{1}-44x^{1}+33x^{0}\right)}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{14x^{2}+44x^{1}-19x^{0}}{\left(2x^{2}-3x^{1}-2\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{14x^{2}+44x-19x^{0}}{\left(2x^{2}-3x-2\right)^{2}}$$

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

$$\frac{14x^{2}+44x-19}{\left(2x^{2}-3x-2\right)^{2}}$$