3/sqrt{5}-frac{2+sqrt{5}}{3sqrt{5}-5} eching

$$\frac{ 3 }{ \sqrt{ 5 } } - \frac{ 2+ \sqrt{ 5 } }{ 3 \sqrt{ 5 } -5 }$$

Baholash

$$\frac{\sqrt{5}-25}{20}\approx -1,138196601$$

Qisqa yechim qadamlari

\frac{3}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{5} kvadrati – 5.

$$\frac{3\sqrt{5}}{5}-\frac{2+\sqrt{5}}{3\sqrt{5}-5}$$

\frac{2+\sqrt{5}}{3\sqrt{5}-5} maxrajini 3\sqrt{5}+5 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(3\sqrt{5}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\left(\sqrt{5}\right)^{2}-5^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\times 5-5^{2}}$$

45 hosil qilish uchun 9 va 5 ni ko'paytirish.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-5^{2}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-25}$$

20 olish uchun 45 dan 25 ni ayirish.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 20 ning eng kichik umumiy karralisi 20. \frac{3\sqrt{5}}{5} ni \frac{4}{4} marotabaga ko'paytirish.

$$\frac{4\times 3\sqrt{5}}{20}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

\frac{4\times 3\sqrt{5}}{20} va \frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5}}{20}$$

12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5} hisob-kitobini qiling.

$$\frac{\sqrt{5}-25}{20}$$