Whakaoti i te {l}{1/x+1=4/3}{text{Solvefor}ytext{where}}{y=1/x+1/x+2}

$$\left. \begin{array} { l } { \frac{1}{x + 1} = \frac{4}{3} }\\ { \text{Solve for } y \text{ where} } \\ { y = \frac{1}{x} + \frac{1}{x + 2} } \end{array} \right.$$

Whakaoti mō x, y

$$y = -\frac{24}{7} = -3\frac{3}{7} \approx -3.428571429$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe x ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+1,3.

$$3=4\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

$$3=4x+4$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$4x+4=3$$

Tangohia te 4 mai i ngā taha e rua.

$$4x=3-4$$

Tangohia te 4 i te 3, ka -1.

$$4x=-1$$

Whakawehea ngā taha e rua ki te 4.

$$x=-\frac{1}{4}$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$y=\frac{1}{-\frac{1}{4}}+\frac{1}{-\frac{1}{4}+2}$$

Whakawehe 1 ki te -\frac{1}{4} mā te whakarea 1 ki te tau huripoki o -\frac{1}{4}.

$$y=1\left(-4\right)+\frac{1}{-\frac{1}{4}+2}$$

Whakareatia te 1 ki te -4, ka -4.

$$y=-4+\frac{1}{-\frac{1}{4}+2}$$

Tāpirihia te -\frac{1}{4} ki te 2, ka \frac{7}{4}.

$$y=-4+\frac{1}{\frac{7}{4}}$$

Whakawehe 1 ki te \frac{7}{4} mā te whakarea 1 ki te tau huripoki o \frac{7}{4}.

$$y=-4+1\times \frac{4}{7}$$

Whakareatia te 1 ki te \frac{4}{7}, ka \frac{4}{7}.

$$y=-4+\frac{4}{7}$$

Tāpirihia te -4 ki te \frac{4}{7}, ka -\frac{24}{7}.

$$y=-\frac{24}{7}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{1}{4} y=-\frac{24}{7}$$