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

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

Whakaoti mō x, y

$$y = -\frac{24}{5} = -4\frac{4}{5} = -4.8$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+2,3.

$$3=4\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+2.

$$3=4x+8$$

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

$$4x+8=3$$

Tangohia te 8 mai i ngā taha e rua.

$$4x=3-8$$

Tangohia te 8 i te 3, ka -5.

$$4x=-5$$

Whakawehea ngā taha e rua ki te 4.

$$x=-\frac{5}{4}$$

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

$$y=\frac{1}{-\frac{5}{4}}+\frac{1}{-\frac{5}{4}+1}$$

Whakawehe 1 ki te -\frac{5}{4} mā te whakarea 1 ki te tau huripoki o -\frac{5}{4}.

$$y=1\left(-\frac{4}{5}\right)+\frac{1}{-\frac{5}{4}+1}$$

Whakareatia te 1 ki te -\frac{4}{5}, ka -\frac{4}{5}.

$$y=-\frac{4}{5}+\frac{1}{-\frac{5}{4}+1}$$

Tāpirihia te -\frac{5}{4} ki te 1, ka -\frac{1}{4}.

$$y=-\frac{4}{5}+\frac{1}{-\frac{1}{4}}$$

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

$$y=-\frac{4}{5}+1\left(-4\right)$$

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

$$y=-\frac{4}{5}-4$$

Tangohia te 4 i te -\frac{4}{5}, ka -\frac{24}{5}.

$$y=-\frac{24}{5}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{5}{4} y=-\frac{24}{5}$$