Réitigh 1/m-n-1/m+n:2/3m-3n

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

Luacháil

$$\frac{2n-3n^{2}+2m+6mn-3m^{2}}{2\left(m^{2}-n^{2}\right)}$$

Céimeanna gearra réitigh

Roinn \frac{1}{m+n} faoi \frac{2}{3m-3n} trí \frac{1}{m+n} a mhéadú faoi dheilín \frac{2}{3m-3n}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de m-n agus \left(m+n\right)\times 2 ná 2\left(m+n\right)\left(m-n\right). Méadaigh \frac{1}{m-n} faoi \frac{2\left(m+n\right)}{2\left(m+n\right)}. Méadaigh \frac{3m-3n}{\left(m+n\right)\times 2} faoi \frac{m-n}{m-n}.

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

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

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

Déan iolrúcháin in 2\left(m+n\right)-\left(3m-3n\right)\left(m-n\right).

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

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

$$\frac{2m+2n-3m^{2}-3n^{2}+6mn}{2\left(m+n\right)\left(m-n\right)}$$

Fairsingigh 2\left(m+n\right)\left(m-n\right)

$$\frac{2m+2n-3m^{2}-3n^{2}+6mn}{2m^{2}-2n^{2}}$$

Fachtóirigh

$$\frac{2n-3n^{2}+2m+6mn-3m^{2}}{2\left(m-n\right)\left(m+n\right)}$$