Whakaoti i te frac{sqrt{3}-5}{sqrt{7}+5}

$$\frac { \sqrt { 3 } - 5 } { \sqrt { 7 } + 5 }$$

Aromātai

$$\frac{5\sqrt{3}+5\sqrt{7}-\sqrt{21}-25}{18}\approx -0.427420283$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{3}-5}{\sqrt{7}+5} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}-5.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)}$$

Whakaarohia te \left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{\left(\sqrt{7}\right)^{2}-5^{2}}$$

Pūrua \sqrt{7}. Pūrua 5.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{7-25}$$

Tangohia te 25 i te 7, ka -18.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{-18}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \sqrt{3}-5 ki ia tau o \sqrt{7}-5.

$$\frac{\sqrt{3}\sqrt{7}-5\sqrt{3}-5\sqrt{7}+25}{-18}$$

Hei whakarea \sqrt{3} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{21}-5\sqrt{3}-5\sqrt{7}+25}{-18}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-\sqrt{21}+5\sqrt{3}+5\sqrt{7}-25}{18}$$