Réitigh (k-1)x^2+3kx+2k-3=0

$$( k - 1 ) x ^ { 2 } + 3 k x + 2 k - 3 = 0$$

Réitigh do k.

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

$$x\neq -2\text{ and }x\neq -1$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun k-1 a mhéadú faoi x^{2}.

$$kx^{2}-x^{2}+3kx+2k-3=0$$

Cuir x^{2} leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

$$kx^{2}+3kx+2k-3=x^{2}$$

Cuir 3 leis an dá thaobh.

$$kx^{2}+3kx+2k=x^{2}+3$$

Comhcheangail na téarmaí ar fad ina bhfuil k.

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

Roinn an dá thaobh faoi x^{2}+3x+2.

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

Má roinntear é faoi x^{2}+3x+2 cuirtear an iolrúchán faoi x^{2}+3x+2 ar ceal.

$$k=\frac{x^{2}+3}{x^{2}+3x+2}$$

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

$$k=\frac{x^{2}+3}{\left(x+1\right)\left(x+2\right)}$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\neq 1\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}+20k-12}-3k}{2\left(k-1\right)}\text{; }x=-\frac{\sqrt{k^{2}+20k-12}+3k}{2\left(k-1\right)}\text{, }&k\leq -4\sqrt{7}-10\text{ or }\left(k\neq 1\text{ and }k\geq 4\sqrt{7}-10\right)\\x=\frac{1}{3}\text{, }&k=1\end{matrix}\right.$$