Réitigh x^2/x^2+x-12

$$\frac { x ^ { 2 } } { x ^ { 2 } + x - 12 }$$

Difreálaigh w.r.t. x

$$\frac{x\left(x-24\right)}{\left(\left(x-3\right)\left(x+4\right)\right)^{2}}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

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.

$$\frac{\left(x^{2}+x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})-x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1}-12)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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}.

$$\frac{\left(x^{2}+x^{1}-12\right)\times 2x^{2-1}-x^{2}\left(2x^{2-1}+x^{1-1}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{\left(x^{2}+x^{1}-12\right)\times 2x^{1}-x^{2}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Méadaigh x^{2}+x^{1}-12 faoi 2x^{1}.

$$\frac{x^{2}\times 2x^{1}+x^{1}\times 2x^{1}-12\times 2x^{1}-x^{2}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Méadaigh x^{2} faoi 2x^{1}+x^{0}.

$$\frac{x^{2}\times 2x^{1}+x^{1}\times 2x^{1}-12\times 2x^{1}-\left(x^{2}\times 2x^{1}+x^{2}x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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

$$\frac{2x^{2+1}+2x^{1+1}-12\times 2x^{1}-\left(2x^{2+1}+x^{2}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Simpligh.

$$\frac{2x^{3}+2x^{2}-24x^{1}-\left(2x^{3}+x^{2}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{x^{2}-24x^{1}}{\left(x^{2}+x^{1}-12\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{x^{2}-24x}{\left(x^{2}+x-12\right)^{2}}$$

Luacháil

$$\frac{x^{2}}{x^{2}+x-12}$$