Réitigh 1/3+1/2n+1-1/2n+3

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

Luacháil

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

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

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

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

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

Cumaisc téarmaí comhchosúla in: 2n+1+3.

$$\frac{2n+4}{3\left(2n+1\right)}-\frac{1}{2n+3}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 3\left(2n+1\right) agus 2n+3 ná 3\left(2n+1\right)\left(2n+3\right). Méadaigh \frac{2n+4}{3\left(2n+1\right)} faoi \frac{2n+3}{2n+3}. Méadaigh \frac{1}{2n+3} faoi \frac{3\left(2n+1\right)}{3\left(2n+1\right)}.

$$\frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)}-\frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)}$$

Tá an t-ainmneoir céanna ag \frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)} agus \frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{\left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)}$$

Déan iolrúcháin in \left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right).

$$\frac{4n^{2}+6n+8n+12-6n-3}{3\left(2n+1\right)\left(2n+3\right)}$$

Cumaisc téarmaí comhchosúla in: 4n^{2}+6n+8n+12-6n-3.

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

Fairsingigh 3\left(2n+1\right)\left(2n+3\right)

$$\frac{4n^{2}+8n+9}{12n^{2}+24n+9}$$

Fachtóirigh

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$