Issolvi r/1-r+x-2/r=1

$$\frac { r } { 1 - r } + \frac { x - 2 } { r } = 1$$

Solvi għal x

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

$$r\neq 1\text{ and }r\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'r\left(r-1\right), l-inqas denominatur komuni ta' 1-r,r.

$$-rr+\left(r-1\right)\left(x-2\right)=r\left(r-1\right)$$

Immultiplika r u r biex tikseb r^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika r-1 b'x-2.

$$-r^{2}+rx-2r-x+2=r\left(r-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika r b'r-1.

$$-r^{2}+rx-2r-x+2=r^{2}-r$$

Żid r^{2} maż-żewġ naħat.

$$rx-2r-x+2=r^{2}-r+r^{2}$$

Ikkombina r^{2} u r^{2} biex tikseb 2r^{2}.

$$rx-2r-x+2=2r^{2}-r$$

Żid 2r maż-żewġ naħat.

$$rx-x+2=2r^{2}-r+2r$$

Ikkombina -r u 2r biex tikseb r.

$$rx-x+2=2r^{2}+r$$

Naqqas 2 miż-żewġ naħat.

$$rx-x=2r^{2}+r-2$$

Ikkombina t-termini kollha li fihom x.

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

Iddividi ż-żewġ naħat b'r-1.

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

Meta tiddividi b'r-1 titneħħa l-multiplikazzjoni b'r-1.

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

Solvi għal r (complex solution)

$$\left\{\begin{matrix}\\r=\frac{\sqrt{x^{2}-10x+17}+x-1}{4}\text{, }&\text{unconditionally}\\r=\frac{-\sqrt{x^{2}-10x+17}+x-1}{4}\text{, }&x\neq 2\end{matrix}\right.$$

Solvi għal r

$$\left\{\begin{matrix}r=\frac{-\sqrt{x^{2}-10x+17}+x-1}{4}\text{, }&\left(x\leq 5-2\sqrt{2}\text{ and }x\neq 2\right)\text{ or }x\geq 2\sqrt{2}+5\\r=\frac{\sqrt{x^{2}-10x+17}+x-1}{4}\text{, }&x\geq 2\sqrt{2}+5\text{ or }x\leq 5-2\sqrt{2}\end{matrix}\right.$$