Lahenda x^2z+10/x+2=3x/x+2

$$\frac { x ^ { 2 } z + 10 } { x + 2 } = \frac { 3 x } { x + 2 }$$

Lahendage ja leidke z

$$z=-\frac{10-3x}{x^{2}}$$

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

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled x+2-ga.

$$x^{2}z+10=3x$$

Lahutage mõlemast poolest 10.

$$x^{2}z=3x-10$$

Jagage mõlemad pooled x^{2}-ga.

$$\frac{x^{2}z}{x^{2}}=\frac{3x-10}{x^{2}}$$

x^{2}-ga jagamine võtab x^{2}-ga korrutamise tagasi.

$$z=\frac{3x-10}{x^{2}}$$

Lahendage ja leidke x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{9-40z}+3}{2z}\text{, }&z\neq 0\\x=\frac{\sqrt{9-40z}+3}{2z}\text{, }&z\neq -4\text{ and }z\neq 0\\x=\frac{10}{3}\approx 3,333333333\text{, }&z=0\end{matrix}\right,$$

Lahendage ja leidke x

$$\left\{\begin{matrix}x=\frac{-\sqrt{9-40z}+3}{2z}\text{, }&z\neq 0\text{ and }z\leq \frac{9}{40}\\x=\frac{\sqrt{9-40z}+3}{2z}\text{, }&z\neq -4\text{ and }z\neq 0\text{ and }z\leq \frac{9}{40}\\x=\frac{10}{3}\approx 3,333333333\text{, }&z=0\end{matrix}\right,$$