Lahenda frac{operatorname{gy}x}{x+1}+x+1/x=13/6

$$\frac { \operatorname { gy } x } { x + 1 } + \frac { x + 1 } { x } = \frac { 13 } { 6 }$$

Lahendage ja leidke g (complex solution)

$$\left\{\begin{matrix}g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\text{ and }x\neq -1\\g\in \mathrm{C}\text{, }&x=\frac{6}{7}\text{ and }y=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled arvuga 6x\left(x+1\right), mis on arvu x+1,x,6 vähim ühiskordne.

$$6xgyx+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

Korrutage x ja x, et leida x^{2}.

$$6x^{2}gy+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

Kasutage distributiivsusomadust, et korrutada 6x+6 ja x+1, ning koondage sarnased liikmed.

$$6x^{2}gy+6x^{2}+12x+6=13x\left(x+1\right)$$

Kasutage distributiivsusomadust, et korrutada 13x ja x+1.

$$6x^{2}gy+6x^{2}+12x+6=13x^{2}+13x$$

Lahutage mõlemast poolest 6x^{2}.

$$6x^{2}gy+12x+6=13x^{2}+13x-6x^{2}$$

Kombineerige 13x^{2} ja -6x^{2}, et leida 7x^{2}.

$$6x^{2}gy+12x+6=7x^{2}+13x$$

Lahutage mõlemast poolest 12x.

$$6x^{2}gy+6=7x^{2}+13x-12x$$

Kombineerige 13x ja -12x, et leida x.

$$6x^{2}gy+6=7x^{2}+x$$

Lahutage mõlemast poolest 6.

$$6x^{2}gy=7x^{2}+x-6$$

Võrrand on standardkujul.

$$6yx^{2}g=7x^{2}+x-6$$

Jagage mõlemad pooled 6x^{2}y-ga.

$$\frac{6yx^{2}g}{6yx^{2}}=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

6x^{2}y-ga jagamine võtab 6x^{2}y-ga korrutamise tagasi.

$$g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

Lahendage ja leidke g

$$\left\{\begin{matrix}g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\text{ and }x\neq -1\\g\in \mathrm{R}\text{, }&x=\frac{6}{7}\text{ and }y=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled arvuga 6x\left(x+1\right), mis on arvu x+1,x,6 vähim ühiskordne.

$$6xgyx+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

Korrutage x ja x, et leida x^{2}.

$$6x^{2}gy+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

Kasutage distributiivsusomadust, et korrutada 6x+6 ja x+1, ning koondage sarnased liikmed.

$$6x^{2}gy+6x^{2}+12x+6=13x\left(x+1\right)$$

Kasutage distributiivsusomadust, et korrutada 13x ja x+1.

$$6x^{2}gy+6x^{2}+12x+6=13x^{2}+13x$$

Lahutage mõlemast poolest 6x^{2}.

$$6x^{2}gy+12x+6=13x^{2}+13x-6x^{2}$$

Kombineerige 13x^{2} ja -6x^{2}, et leida 7x^{2}.

$$6x^{2}gy+12x+6=7x^{2}+13x$$

Lahutage mõlemast poolest 12x.

$$6x^{2}gy+6=7x^{2}+13x-12x$$

Kombineerige 13x ja -12x, et leida x.

$$6x^{2}gy+6=7x^{2}+x$$

Lahutage mõlemast poolest 6.

$$6x^{2}gy=7x^{2}+x-6$$

Võrrand on standardkujul.

$$6yx^{2}g=7x^{2}+x-6$$

Jagage mõlemad pooled 6x^{2}y-ga.

$$\frac{6yx^{2}g}{6yx^{2}}=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

6x^{2}y-ga jagamine võtab 6x^{2}y-ga korrutamise tagasi.

$$g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

Lahendage ja leidke x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{169-144gy}-13}{12gy+\sqrt{169-144gy}-13}\text{, }&y\neq 0\text{ and }g\neq 0\\x=\frac{\sqrt{169-144gy}+13}{12gy-\sqrt{169-144gy}-13}\text{, }&g\neq \frac{7}{6y}\text{ and }y\neq 0\text{ and }g\neq 0\\x=\frac{6}{7}\text{, }&y=0\text{ or }g=0\end{matrix}\right,$$