Resolver (k-1)x^2+3kx+2k-3=0

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

Resolver k

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

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

Pasos para resolver unha ecuación lineal

Usa a propiedade distributiva para multiplicar k-1 por x^{2}.

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

Engadir x^{2} en ambos lados. Calquera valor máis cero é igual ao valor.

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

Engadir 3 en ambos lados.

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

Combina todos os termos que conteñan k.

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

Divide ambos lados entre x^{2}+3x+2.

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

A división entre x^{2}+3x+2 desfai a multiplicación por x^{2}+3x+2.

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

Divide x^{2}+3 entre x^{2}+3x+2.

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

Resolver x (complex solution)

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

Resolver x

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