Réitigh 1/1-r-r/1-r^2

$$\frac { 1 } { 1 - r } - \frac { r } { 1 - r ^ { 2 } }$$

Luacháil

$$\frac{1}{1-r^{2}}$$

Céimeanna gearra réitigh

Fachtóirigh 1-r^{2}.

$$\frac{1}{1-r}-\frac{r}{\left(r-1\right)\left(-r-1\right)}$$

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

$$\frac{-\left(r+1\right)}{\left(r-1\right)\left(r+1\right)}-\frac{-r}{\left(r-1\right)\left(r+1\right)}$$

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

$$\frac{-\left(r+1\right)-\left(-r\right)}{\left(r-1\right)\left(r+1\right)}$$

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

$$\frac{-r-1+r}{\left(r-1\right)\left(r+1\right)}$$

Cumaisc téarmaí comhchosúla in: -r-1+r.

$$\frac{-1}{\left(r-1\right)\left(r+1\right)}$$

Fairsingigh \left(r-1\right)\left(r+1\right)

$$\frac{-1}{r^{2}-1}$$

Difreálaigh w.r.t. r

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