frac{sqrt{3}-3}{sqrt{3}+3} eching

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

Baholash

$$\sqrt{3}-2\approx -0,267949192$$

Yechim qadamlari

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

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

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

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

\sqrt{3} kvadratini chiqarish. 3 kvadratini chiqarish.

$$\frac{\left(\sqrt{3}-3\right)\left(\sqrt{3}-3\right)}{3-9}$$

-6 olish uchun 3 dan 9 ni ayirish.

$$\frac{\left(\sqrt{3}-3\right)\left(\sqrt{3}-3\right)}{-6}$$

\left(\sqrt{3}-3\right)^{2} hosil qilish uchun \sqrt{3}-3 va \sqrt{3}-3 ni ko'paytirish.

$$\frac{\left(\sqrt{3}-3\right)^{2}}{-6}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{3}-3\right)^{2} kengaytirilishi uchun ishlating.

$$\frac{\left(\sqrt{3}\right)^{2}-6\sqrt{3}+9}{-6}$$

\sqrt{3} kvadrati – 3.

$$\frac{3-6\sqrt{3}+9}{-6}$$

12 olish uchun 3 va 9'ni qo'shing.

$$\frac{12-6\sqrt{3}}{-6}$$

-2+\sqrt{3} natijani olish uchun 12-6\sqrt{3} ning har bir ifodasini -6 ga bo‘ling.

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