Réitigh (x-2)(xy-1)=5

$$( x - 2 ) ( x y - 1 ) = 5$$

Réitigh do y.

$$y=\frac{x+3}{x\left(x-2\right)}$$

$$x\neq 2\text{ and }x\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun x-2 a mhéadú faoi xy-1.

$$yx^{2}-x-2xy+2=5$$

Cuir x leis an dá thaobh.

$$yx^{2}-2xy+2=5+x$$

Bain 2 ón dá thaobh.

$$yx^{2}-2xy=5+x-2$$

Dealaigh 2 ó 5 chun 3 a fháil.

$$yx^{2}-2xy=3+x$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(x^{2}-2x\right)y=3+x$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x^{2}-2x\right)y=x+3$$

Roinn an dá thaobh faoi x^{2}-2x.

$$\frac{\left(x^{2}-2x\right)y}{x^{2}-2x}=\frac{x+3}{x^{2}-2x}$$

Má roinntear é faoi x^{2}-2x cuirtear an iolrúchán faoi x^{2}-2x ar ceal.

$$y=\frac{x+3}{x^{2}-2x}$$

Roinn x+3 faoi x^{2}-2x.

$$y=\frac{x+3}{x\left(x-2\right)}$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4y^{2}+16y+1}+2y+1}{2y}\text{; }x=\frac{-\sqrt{4y^{2}+16y+1}+2y+1}{2y}\text{, }&y\neq 0\\x=-3\text{, }&y=0\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}x=\frac{\sqrt{4y^{2}+16y+1}+2y+1}{2y}\text{; }x=\frac{-\sqrt{4y^{2}+16y+1}+2y+1}{2y}\text{, }&y\leq -\frac{\sqrt{15}}{2}-2\text{ or }\left(y\neq 0\text{ and }y\geq \frac{\sqrt{15}}{2}-2\right)\\x=-3\text{, }&y=0\end{matrix}\right.$$