Whakaoti i te (11/9-x):x=17/3:34/5

$$( \frac { 11 } { 9 } - x ) : x = \frac { 17 } { 3 } : \frac { 34 } { 5 }$$

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$\frac{11}{9}-x=x\times \frac{\frac{17}{3}}{\frac{34}{5}}$$

Whakawehe \frac{17}{3} ki te \frac{34}{5} mā te whakarea \frac{17}{3} ki te tau huripoki o \frac{34}{5}.

$$\frac{11}{9}-x=x\times \frac{17}{3}\times \frac{5}{34}$$

Me whakarea te \frac{17}{3} ki te \frac{5}{34} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{11}{9}-x=x\times \frac{17\times 5}{3\times 34}$$

Mahia ngā whakarea i roto i te hautanga \frac{17\times 5}{3\times 34}.

$$\frac{11}{9}-x=x\times \frac{85}{102}$$

Whakahekea te hautanga \frac{85}{102} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 17.

$$\frac{11}{9}-x=x\times \frac{5}{6}$$

Tangohia te x\times \frac{5}{6} mai i ngā taha e rua.

$$\frac{11}{9}-x-x\times \frac{5}{6}=0$$

Pahekotia te -x me -x\times \frac{5}{6}, ka -\frac{11}{6}x.

$$\frac{11}{9}-\frac{11}{6}x=0$$

Tangohia te \frac{11}{9} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{11}{6}x=-\frac{11}{9}$$

Me whakarea ngā taha e rua ki te -\frac{6}{11}, te tau utu o -\frac{11}{6}.

$$x=-\frac{11}{9}\left(-\frac{6}{11}\right)$$

Me whakarea te -\frac{11}{9} ki te -\frac{6}{11} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-11\left(-6\right)}{9\times 11}$$

Mahia ngā whakarea i roto i te hautanga \frac{-11\left(-6\right)}{9\times 11}.

$$x=\frac{66}{99}$$

Whakahekea te hautanga \frac{66}{99} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 33.

$$x=\frac{2}{3}$$