Issolvi 6*f(x)=x+1/x-2

$$6 \cdot f ( x ) = \frac { x + 1 } { x - 2 }$$

Solvi għal f

$$f=\frac{x+1}{6x\left(x-2\right)}$$

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x-2.

$$6fx\left(x-2\right)=x+1$$

Uża l-propjetà distributtiva biex timmultiplika 6fx b'x-2.

$$6fx^{2}-12fx=x+1$$

Ikkombina t-termini kollha li fihom f.

$$\left(6x^{2}-12x\right)f=x+1$$

Iddividi ż-żewġ naħat b'6x^{2}-12x.

$$\frac{\left(6x^{2}-12x\right)f}{6x^{2}-12x}=\frac{x+1}{6x^{2}-12x}$$

Meta tiddividi b'6x^{2}-12x titneħħa l-multiplikazzjoni b'6x^{2}-12x.

$$f=\frac{x+1}{6x^{2}-12x}$$

Iddividi x+1 b'6x^{2}-12x.

$$f=\frac{x+1}{6x\left(x-2\right)}$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{144f^{2}+48f+1}+12f+1}{12f}\text{; }x=\frac{-\sqrt{144f^{2}+48f+1}+12f+1}{12f}\text{, }&f\neq 0\\x=-1\text{, }&f=0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{\sqrt{144f^{2}+48f+1}+12f+1}{12f}\text{; }x=\frac{-\sqrt{144f^{2}+48f+1}+12f+1}{12f}\text{, }&f\leq -\frac{\sqrt{3}}{12}-\frac{1}{6}\text{ or }\left(f\neq 0\text{ and }f\geq \frac{\sqrt{3}}{12}-\frac{1}{6}\right)\\x=-1\text{, }&f=0\end{matrix}\right.$$