Réitigh 2mn/m^3+n^3+2m/m^2-n^2-1/m-n

$$\frac { 2 m n } { m ^ { 3 } + n ^ { 3 } } + \frac { 2 m } { m ^ { 2 } - n ^ { 2 } } - \frac { 1 } { m - n }$$

Luacháil

$$\frac{m^{2}+mn+n^{2}}{m^{3}+n^{3}}$$

Céimeanna gearra réitigh

Fachtóirigh m^{3}+n^{3}. Fachtóirigh m^{2}-n^{2}.

$$\frac{2mn}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}+\frac{2m}{\left(m+n\right)\left(m-n\right)}-\frac{1}{m-n}$$

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(m+n\right)\left(m^{2}-mn+n^{2}\right) agus \left(m+n\right)\left(m-n\right) ná \left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right). Méadaigh \frac{2mn}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)} faoi \frac{m-n}{m-n}. Méadaigh \frac{2m}{\left(m+n\right)\left(m-n\right)} faoi \frac{m^{2}-mn+n^{2}}{m^{2}-mn+n^{2}}.

$$\frac{2mn\left(m-n\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}+\frac{2m\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

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

$$\frac{2mn\left(m-n\right)+2m\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

Déan iolrúcháin in 2mn\left(m-n\right)+2m\left(m^{2}-mn+n^{2}\right).

$$\frac{2m^{2}n-2mn^{2}+2m^{3}-2m^{2}n+2mn^{2}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

Cumaisc téarmaí comhchosúla in: 2m^{2}n-2mn^{2}+2m^{3}-2m^{2}n+2mn^{2}.

$$\frac{2m^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

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(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right) agus m-n ná \left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right). Méadaigh \frac{1}{m-n} faoi \frac{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}.

$$\frac{2m^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}$$

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

$$\frac{2m^{3}-\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}$$

Déan iolrúcháin in 2m^{3}-\left(m+n\right)\left(m^{2}-mn+n^{2}\right).

$$\frac{2m^{3}-m^{3}+m^{2}n-mn^{2}-nm^{2}+n^{2}m-n^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}$$

Cumaisc téarmaí comhchosúla in: 2m^{3}-m^{3}+m^{2}n-mn^{2}-nm^{2}+n^{2}m-n^{3}.

$$\frac{m^{3}-n^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{m^{3}-n^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}.

$$\frac{\left(m-n\right)\left(m^{2}+mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}$$

Cealaigh m-n mar uimhreoir agus ainmneoir.

$$\frac{m^{2}+mn+n^{2}}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}$$

Fairsingigh \left(m+n\right)\left(m^{2}-mn+n^{2}\right)

$$\frac{m^{2}+mn+n^{2}}{m^{3}+n^{3}}$$

Difreálaigh w.r.t. m

$$\frac{-m^{4}+2mn^{3}+n^{4}-2nm^{3}-3\left(mn\right)^{2}}{\left(m^{3}+n^{3}\right)^{2}}$$