Solve s*x^r-r(a-r)x+1r-a=0

$$s \cdot x ^ { r } - r ( a - r ) x + 1 r - a = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{xr^{2}+sx^{r}+r}{rx+1}\text{, }&r=0\text{ or }x\neq -\frac{1}{r}\\a\in \mathrm{C}\text{, }&s=0\text{ and }x=-\frac{1}{r}\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply r by a-r.

$$sx^{r}-\left(ra-r^{2}\right)x+1r-a=0$$

Use the distributive property to multiply ra-r^{2} by x.

$$sx^{r}-\left(rax-r^{2}x\right)+1r-a=0$$

To find the opposite of rax-r^{2}x, find the opposite of each term.

$$sx^{r}-rax+r^{2}x+1r-a=0$$

Subtract sx^{r} from both sides. Anything subtracted from zero gives its negation.

$$-rax+r^{2}x+1r-a=-sx^{r}$$

Subtract r^{2}x from both sides.

$$-rax+1r-a=-sx^{r}-r^{2}x$$

Subtract 1r from both sides.

$$-rax-a=-sx^{r}-r^{2}x-r$$

Reorder the terms.

$$-arx-a=-xr^{2}-sx^{r}-r$$

Combine all terms containing a.

$$\left(-rx-1\right)a=-xr^{2}-sx^{r}-r$$

Divide both sides by -rx-1.

$$\frac{\left(-rx-1\right)a}{-rx-1}=\frac{-xr^{2}-sx^{r}-r}{-rx-1}$$

Dividing by -rx-1 undoes the multiplication by -rx-1.

$$a=\frac{-xr^{2}-sx^{r}-r}{-rx-1}$$

Divide -xr^{2}-sx^{r}-r by -rx-1.

$$a=\frac{xr^{2}+sx^{r}+r}{rx+1}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{xr^{2}+sx^{r}+r}{rx+1}\text{, }&\left(r=0\text{ and }x\neq 0\right)\text{ or }\left(x\neq -\frac{1}{r}\text{ and }x<0\text{ and }Denominator(r)\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }r>0\right)\text{ or }\left(x\neq -\frac{1}{r}\text{ and }x>0\right)\\a\in \mathrm{R}\text{, }&r\neq 0\text{ and }\left(r<0\text{ or }Denominator(r)\text{bmod}2=1\right)\text{ and }s=0\text{ and }x=-\frac{1}{r}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply r by a-r.

$$sx^{r}-\left(ra-r^{2}\right)x+1r-a=0$$

Use the distributive property to multiply ra-r^{2} by x.

$$sx^{r}-\left(rax-r^{2}x\right)+1r-a=0$$

To find the opposite of rax-r^{2}x, find the opposite of each term.

$$sx^{r}-rax+r^{2}x+1r-a=0$$

Subtract sx^{r} from both sides. Anything subtracted from zero gives its negation.

$$-rax+r^{2}x+1r-a=-sx^{r}$$

Subtract r^{2}x from both sides.

$$-rax+1r-a=-sx^{r}-r^{2}x$$

Subtract 1r from both sides.

$$-rax-a=-sx^{r}-r^{2}x-r$$

Reorder the terms.

$$-arx-a=-xr^{2}-sx^{r}-r$$

Combine all terms containing a.

$$\left(-rx-1\right)a=-xr^{2}-sx^{r}-r$$

Divide both sides by -rx-1.

$$\frac{\left(-rx-1\right)a}{-rx-1}=\frac{-xr^{2}-sx^{r}-r}{-rx-1}$$

Dividing by -rx-1 undoes the multiplication by -rx-1.

$$a=\frac{-xr^{2}-sx^{r}-r}{-rx-1}$$

Divide -xr^{2}-sx^{r}-r by -rx-1.

$$a=\frac{xr^{2}+sx^{r}+r}{rx+1}$$