Réitigh 1/(2n-1)^2+1/4n^2

$$\frac { 1 } { ( 2 n - 1 ) ^ { 2 } } + \frac { 1 } { 4 n ^ { 2 } }$$

Luacháil

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

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 \left(2n-1\right)^{2} agus 4n^{2} ná 4n^{2}\left(2n-1\right)^{2}. Méadaigh \frac{1}{\left(2n-1\right)^{2}} faoi \frac{4n^{2}}{4n^{2}}. Méadaigh \frac{1}{4n^{2}} faoi \frac{\left(2n-1\right)^{2}}{\left(2n-1\right)^{2}}.

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

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

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

Déan iolrúcháin in 4n^{2}+\left(2n-1\right)^{2}.

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

Cumaisc téarmaí comhchosúla in: 4n^{2}+4n^{2}-4n+1.

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

Fairsingigh 4n^{2}\left(2n-1\right)^{2}

$$\frac{8n^{2}-4n+1}{16n^{4}-16n^{3}+4n^{2}}$$

Fairsingigh

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

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 \left(2n-1\right)^{2} agus 4n^{2} ná 4n^{2}\left(2n-1\right)^{2}. Méadaigh \frac{1}{\left(2n-1\right)^{2}} faoi \frac{4n^{2}}{4n^{2}}. Méadaigh \frac{1}{4n^{2}} faoi \frac{\left(2n-1\right)^{2}}{\left(2n-1\right)^{2}}.

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

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

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

Déan iolrúcháin in 4n^{2}+\left(2n-1\right)^{2}.

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

Cumaisc téarmaí comhchosúla in: 4n^{2}+4n^{2}-4n+1.

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

Fairsingigh 4n^{2}\left(2n-1\right)^{2}

$$\frac{8n^{2}-4n+1}{16n^{4}-16n^{3}+4n^{2}}$$