Réitigh 1/(1+t)^2+1/(1-t^2)

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

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh 1-t^{2}.

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

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

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

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

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

Déan iolrúcháin in t-1-\left(t+1\right).

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

Cumaisc téarmaí comhchosúla in: t-1-t-1.

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

Fairsingigh \left(t-1\right)\left(t+1\right)^{2}

$$\frac{-2}{t^{3}+t^{2}-t-1}$$

Fairsingigh

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

Céimeanna gearra réitigh

Fachtóirigh 1-t^{2}.

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

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

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

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

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

Déan iolrúcháin in t-1-\left(t+1\right).

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

Cumaisc téarmaí comhchosúla in: t-1-t-1.

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

Fairsingigh \left(t-1\right)\left(t+1\right)^{2}

$$\frac{-2}{t^{3}+t^{2}-t-1}$$