Réitigh a/1-a^2+a/1+a^2=

$$\frac { a } { 1 - a ^ { 2 } } + \frac { a } { 1 + a ^ { 2 } } =$$

Luacháil

$$\frac{2a}{1-a^{4}}$$

Céimeanna gearra réitigh

Fachtóirigh 1-a^{2}.

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

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

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

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

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

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

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

Cumaisc téarmaí comhchosúla in: a^{3}+a-a^{3}-a^{2}+a^{2}+a.

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

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

$$\frac{2a}{-a^{4}+1}$$

Fachtóirigh

$$\frac{2a}{1-a^{4}}$$