1(1-1/1-frac{1{x}})=20191 eching

$$1 ( 1 - \frac { 1 } { 1 - \frac { 1 } { x } } ) = 20191$$

x uchun yechish

$$x=\frac{20190}{20191}\approx 0,999950473$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikki tarafini 1 ga bo‘ling.

$$1-\frac{1}{1-\frac{1}{x}}=20191$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x}{x} marotabaga ko'paytirish.

$$1-\frac{1}{\frac{x}{x}-\frac{1}{x}}=20191$$

\frac{x}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$1-\frac{1}{\frac{x-1}{x}}=20191$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{x-1}{x} ga bo'lish 1 ga k'paytirish \frac{x-1}{x} ga qaytarish.

$$1-\frac{x}{x-1}=20191$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{x-1}{x-1}-\frac{x}{x-1}=20191$$

\frac{x-1}{x-1} va \frac{x}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x-1-x}{x-1}=20191$$

x-1-x kabi iboralarga o‘xshab birlashtiring.

$$\frac{-1}{x-1}=20191$$

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$-1=20191\left(x-1\right)$$

Ikki tarafini 20191 ga bo‘ling.

$$-\frac{1}{20191}=x-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x-1=-\frac{1}{20191}$$

1 ni ikki tarafga qo’shing.

$$x=-\frac{1}{20191}+1$$

\frac{20190}{20191} olish uchun -\frac{1}{20191} va 1'ni qo'shing.

$$x=\frac{20190}{20191}$$