Réitigh 2/x-5-5/x+3

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

Luacháil

$$\frac{31-3x}{\left(x-5\right)\left(x+3\right)}$$

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

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

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

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

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

$$\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)}$$

Cumaisc téarmaí comhchosúla in: 2x+6-5x+25.

$$\frac{-3x+31}{\left(x-5\right)\left(x+3\right)}$$

Fairsingigh \left(x-5\right)\left(x+3\right)

$$\frac{-3x+31}{x^{2}-2x-15}$$

Difreálaigh w.r.t. x

$$\frac{3x^{2}-62x+107}{x^{4}-4x^{3}-26x^{2}+60x+225}$$

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)})$$

Cumaisc téarmaí comhchosúla in: 2x+6-5x+25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{\left(x-5\right)\left(x+3\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-5 a iolrú faoi gach téarma de x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}+3x-5x-15})$$

Comhcheangail 3x agus -5x chun -2x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}-2x-15})$$

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.

$$\frac{\left(x^{2}-2x^{1}-15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{1}+31)-\left(-3x^{1}+31\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}-15)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{1-1}-\left(-3x^{1}+31\right)\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Méadaigh x^{2}-2x^{1}-15 faoi -3x^{0}.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Méadaigh -3x^{1}+31 faoi 2x^{1}-2x^{0}.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}\times 2x^{1}-3x^{1}\left(-2\right)x^{0}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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

$$\frac{-3x^{2}-2\left(-3\right)x^{1}-15\left(-3\right)x^{0}-\left(-3\times 2x^{1+1}-3\left(-2\right)x^{1}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Simpligh.

$$\frac{-3x^{2}+6x^{1}+45x^{0}-\left(-6x^{2}+6x^{1}+62x^{1}-62x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{3x^{2}-62x^{1}+107x^{0}}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{3x^{2}-62x+107x^{0}}{\left(x^{2}-2x-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107\times 1}{\left(x^{2}-2x-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107}{\left(x^{2}-2x-15\right)^{2}}$$