(x+1/x)^2-(x-1/x)^2 eching

$$( x + \frac { 1 } { x } ) ^ { 2 } - ( \frac { x - 1 } { x } ) ^ { 2 }$$

Baholash

$$\frac{x^{3}+x+2}{x}$$

Qisqa yechim qadamlari

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

$$\left(\frac{xx}{x}+\frac{1}{x}\right)^{2}-\left(\frac{x-1}{x}\right)^{2}$$

\frac{xx}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\left(\frac{xx+1}{x}\right)^{2}-\left(\frac{x-1}{x}\right)^{2}$$

xx+1 ichidagi ko‘paytirishlarni bajaring.

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

\frac{x^{2}+1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

\frac{x-1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

\left(x^{2}+1\right)^{2}-\left(x-1\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{4}+2x^{2}+1-x^{2}+2x-1}{x^{2}}$$

x^{4}+2x^{2}+1-x^{2}+2x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{4}+x^{2}+2x}{x^{2}}$$

\frac{x^{4}+x^{2}+2x}{x^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

x+1 ga x^{2}-x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{x^{3}+x+2}{x}$$

Kengaytirish

$$\frac{x^{3}+x+2}{x}$$

Qisqa yechim qadamlari

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

$$\left(\frac{xx}{x}+\frac{1}{x}\right)^{2}-\left(\frac{x-1}{x}\right)^{2}$$

\frac{xx}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\left(\frac{xx+1}{x}\right)^{2}-\left(\frac{x-1}{x}\right)^{2}$$

xx+1 ichidagi ko‘paytirishlarni bajaring.

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

\frac{x^{2}+1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

\frac{x-1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

\left(x^{2}+1\right)^{2}-\left(x-1\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{4}+2x^{2}+1-x^{2}+2x-1}{x^{2}}$$

x^{4}+2x^{2}+1-x^{2}+2x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{4}+x^{2}+2x}{x^{2}}$$

\frac{x^{4}+x^{2}+2x}{x^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

x+1 ga x^{2}-x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{x^{3}+x+2}{x}$$