Réitigh 1/sqrt{x}=1/2y+1/3z

$$\frac{ 1 }{ \sqrt{ x } } = \frac{ 1 }{ 2y } + \frac{ 1 }{ 3z }$$

Réitigh do y.

$$y=-\frac{3\sqrt{x}z}{2\left(-3z+\sqrt{x}\right)}$$

$$z\neq 0\text{ and }\left(z<0\text{ or }x\neq 9z^{2}\right)\text{ and }x>0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg y a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Iolraigh an dá thaobh den chothromóid faoi 6yz, an comhiolraí is lú de 2y,3z.

$$6yzx^{-\frac{1}{2}}=3z+2y$$

Bain 2y ón dá thaobh.

$$6yzx^{-\frac{1}{2}}-2y=3z$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(6zx^{-\frac{1}{2}}-2\right)y=3z$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(\frac{6z}{\sqrt{x}}-2\right)y=3z$$

Roinn an dá thaobh faoi 6zx^{-\frac{1}{2}}-2.

$$\frac{\left(\frac{6z}{\sqrt{x}}-2\right)y}{\frac{6z}{\sqrt{x}}-2}=\frac{3z}{\frac{6z}{\sqrt{x}}-2}$$

Má roinntear é faoi 6zx^{-\frac{1}{2}}-2 cuirtear an iolrúchán faoi 6zx^{-\frac{1}{2}}-2 ar ceal.

$$y=\frac{3z}{\frac{6z}{\sqrt{x}}-2}$$

Roinn 3z faoi 6zx^{-\frac{1}{2}}-2.

$$y=\frac{3\sqrt{x}z}{2\left(3z-\sqrt{x}\right)}$$

Ní féidir leis an athróg y a bheith comhionann le 0.

$$y=\frac{3\sqrt{x}z}{2\left(3z-\sqrt{x}\right)}\text{, }y\neq 0$$

Réitigh do x.

$$x=36\times \left(\frac{yz}{2y+3z}\right)^{2}$$

$$\left(y>0\text{ and }y<-\frac{3z}{2}\right)\text{ or }\left(z>0\text{ and }y<-\frac{3z}{2}\right)\text{ or }\left(z>0\text{ and }y>0\right)$$