Réitigh 2r/r^2-1-1/r+1

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

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh r^{2}-1.

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

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

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

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

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

Déan iolrúcháin in 2r-\left(r-1\right).

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

Cumaisc téarmaí comhchosúla in: 2r-r+1.

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

Cealaigh r+1 mar uimhreoir agus ainmneoir.

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

Difreálaigh w.r.t. r

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

Céimeanna ag Baint Úsáid as an Riail Slabhra

Fachtóirigh r^{2}-1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{\left(r-1\right)\left(r+1\right)}-\frac{1}{r+1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{\left(r-1\right)\left(r+1\right)}-\frac{r-1}{\left(r-1\right)\left(r+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r-\left(r-1\right)}{\left(r-1\right)\left(r+1\right)})$$

Déan iolrúcháin in 2r-\left(r-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r-r+1}{\left(r-1\right)\left(r+1\right)})$$

Cumaisc téarmaí comhchosúla in: 2r-r+1.

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

Cealaigh r+1 mar uimhreoir agus ainmneoir.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{r-1})$$

Más F comhshuíomh dhá fheidhm indifreáilte f\left(u\right) agus u=g\left(x\right), is é sin, más F\left(x\right)=f\left(g\left(x\right)\right), mar sin is ionann díorthach F agus díorthach f maidir le u méadaithe faoi dhíorthach g maidir le x, is é sin, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

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

Simpligh.

$$-r^{0}\left(r^{1}-1\right)^{-2}$$

Do théarma ar bith t, t^{1}=t.

$$-r^{0}\left(r-1\right)^{-2}$$

Do théarma ar bith t ach amháin 0, t^{0}=1.

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