1/1+t+1/1-t-2/3t^2= eching

$$\frac { \frac { 1 } { 1 + t } + \frac { 1 } { 1 - t } - 2 } { 3 t ^ { 2 } } =$$

Baholash

$$\frac{2}{3\left(1-t^{2}\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1+t va 1-t ning eng kichik umumiy karralisi \left(t+1\right)\left(-t+1\right). \frac{1}{1+t} ni \frac{-t+1}{-t+1} marotabaga ko'paytirish. \frac{1}{1-t} ni \frac{t+1}{t+1} marotabaga ko'paytirish.

$$\frac{\frac{-t+1}{\left(t+1\right)\left(-t+1\right)}+\frac{t+1}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

\frac{-t+1}{\left(t+1\right)\left(-t+1\right)} va \frac{t+1}{\left(t+1\right)\left(-t+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-t+1+t+1}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

-t+1+t+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{2}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)} marotabaga ko'paytirish.

$$\frac{\frac{2}{\left(t+1\right)\left(-t+1\right)}-\frac{2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

\frac{2}{\left(t+1\right)\left(-t+1\right)} va \frac{2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{2-2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

2-2\left(t+1\right)\left(-t+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{2+2t^{2}-2t+2t-2}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

2+2t^{2}-2t+2t-2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

\frac{\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}} ni yagona kasrga aylantiring.

$$\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)\times 3t^{2}}$$

Surat va maxrajdagi ikkala t^{2} ni qisqartiring.

$$\frac{2}{3\left(t+1\right)\left(-t+1\right)}$$

3 ga t+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{\left(3t+3\right)\left(-t+1\right)}$$

3t+3 ga -t+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{2}{-3t^{2}+3}$$

Kengaytirish

$$\frac{2}{3\left(1-t^{2}\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1+t va 1-t ning eng kichik umumiy karralisi \left(t+1\right)\left(-t+1\right). \frac{1}{1+t} ni \frac{-t+1}{-t+1} marotabaga ko'paytirish. \frac{1}{1-t} ni \frac{t+1}{t+1} marotabaga ko'paytirish.

$$\frac{\frac{-t+1}{\left(t+1\right)\left(-t+1\right)}+\frac{t+1}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

\frac{-t+1}{\left(t+1\right)\left(-t+1\right)} va \frac{t+1}{\left(t+1\right)\left(-t+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-t+1+t+1}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

-t+1+t+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{2}{\left(t+1\right)\left(-t+1\right)}-2}{3t^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)} marotabaga ko'paytirish.

$$\frac{\frac{2}{\left(t+1\right)\left(-t+1\right)}-\frac{2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

\frac{2}{\left(t+1\right)\left(-t+1\right)} va \frac{2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{2-2\left(t+1\right)\left(-t+1\right)}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

2-2\left(t+1\right)\left(-t+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{2+2t^{2}-2t+2t-2}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

2+2t^{2}-2t+2t-2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}}$$

\frac{\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)}}{3t^{2}} ni yagona kasrga aylantiring.

$$\frac{2t^{2}}{\left(t+1\right)\left(-t+1\right)\times 3t^{2}}$$

Surat va maxrajdagi ikkala t^{2} ni qisqartiring.

$$\frac{2}{3\left(t+1\right)\left(-t+1\right)}$$

3 ga t+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{\left(3t+3\right)\left(-t+1\right)}$$

3t+3 ga -t+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{2}{-3t^{2}+3}$$