Whakaoti i te 1/x-1/y=1/ztext{find}xtext{given}y=5text{and}z=2

$$\frac { 1 } { x } - \frac { 1 } { y } = \frac { 1 } { z } \text { find } x \text { given } y = 5 \text { and } z = 2$$

Whakaoti mō x, y, z

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

$$y=5$$

$$z=2$$

Ngā Upane Otinga

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

$$\frac{1}{x}-\frac{1}{5}=\frac{1}{2}$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10x, arā, te tauraro pātahi he tino iti rawa te kitea o x,5,2.

$$10-2x=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$10-2x-5x=0$$

Pahekotia te -2x me -5x, ka -7x.

$$10-7x=0$$

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-7x=-10$$

Whakawehea ngā taha e rua ki te -7.

$$x=\frac{-10}{-7}$$

Ka taea te hautanga \frac{-10}{-7} te whakamāmā ki te \frac{10}{7} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{10}{7}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{10}{7} y=5 z=2$$