(2x^2-1/(x-2)(x+1))^2-8(2x^2-1)+7(x-1)(x+2) eching

$$( 2 x ^ { 2 } - \frac { 1 } { ( x - 2 ) ( x + 1 ) } ) ^ { 2 } - 8 ( 2 x ^ { 2 } - 1 ) + 7 ( x - 1 ) ( x + 2 )$$

Baholash

$$\frac{4x^{8}-8x^{7}-21x^{6}+41x^{5}+19x^{4}-41x^{3}+18x^{2}+4x-23}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x^{2} ni \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} marotabaga ko'paytirish.

$$\left(\frac{2x^{2}\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

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

$$\left(\frac{2x^{2}\left(x-2\right)\left(x+1\right)-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

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

$$\left(\frac{2x^{4}+2x^{3}-4x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

2x^{4}+2x^{3}-4x^{3}-4x^{2}-1 kabi iboralarga o‘xshab birlashtiring.

$$\left(\frac{2x^{4}-2x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

\frac{2x^{4}-2x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

\left(\left(x-2\right)\left(x+1\right)\right)^{2} ni kengaytirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

-8 ga 2x^{2}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+7\left(x-1\right)\left(x+2\right)$$

7 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+\left(7x-7\right)\left(x+2\right)$$

7x-7 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+7x^{2}+7x-14$$

-9x^{2} ni olish uchun -16x^{2} va 7x^{2} ni birlashtirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-9x^{2}+8+7x-14$$

-6 olish uchun 8 dan 14 ni ayirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-9x^{2}-6+7x$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -9x^{2}-6+7x ni \frac{\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} marotabaga ko'paytirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}+\frac{\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} va \frac{\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}+\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}+\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{8}-4x^{7}-8x^{6}-2x^{4}-4x^{7}+4x^{6}+8x^{5}+2x^{3}-8x^{6}+8x^{5}+16x^{4}+4x^{2}-2x^{4}+2x^{3}+4x^{2}+1-9x^{6}+18x^{5}+27x^{4}-36x^{3}-36x^{2}-6x^{4}+12x^{3}+18x^{2}-24x-24+7x^{5}-14x^{4}-21x^{3}+28x^{2}+28x}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

4x^{8}-4x^{7}-8x^{6}-2x^{4}-4x^{7}+4x^{6}+8x^{5}+2x^{3}-8x^{6}+8x^{5}+16x^{4}+4x^{2}-2x^{4}+2x^{3}+4x^{2}+1-9x^{6}+18x^{5}+27x^{4}-36x^{3}-36x^{2}-6x^{4}+12x^{3}+18x^{2}-24x-24+7x^{5}-14x^{4}-21x^{3}+28x^{2}+28x kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{8}-8x^{7}-21x^{6}+19x^{4}+41x^{5}-41x^{3}+18x^{2}-23+4x}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\left(x-2\right)^{2}\left(x+1\right)^{2} ni kengaytirish.

$$\frac{4x^{8}-8x^{7}-21x^{6}+19x^{4}+41x^{5}-41x^{3}+18x^{2}-23+4x}{x^{4}-2x^{3}-3x^{2}+4x+4}$$

Kengaytirish

$$\frac{4x^{8}-8x^{7}-21x^{6}+41x^{5}+19x^{4}-41x^{3}+18x^{2}+4x-23}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x^{2} ni \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} marotabaga ko'paytirish.

$$\left(\frac{2x^{2}\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

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

$$\left(\frac{2x^{2}\left(x-2\right)\left(x+1\right)-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

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

$$\left(\frac{2x^{4}+2x^{3}-4x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

2x^{4}+2x^{3}-4x^{3}-4x^{2}-1 kabi iboralarga o‘xshab birlashtiring.

$$\left(\frac{2x^{4}-2x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}\right)^{2}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

\frac{2x^{4}-2x^{3}-4x^{2}-1}{\left(x-2\right)\left(x+1\right)}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

\left(\left(x-2\right)\left(x+1\right)\right)^{2} ni kengaytirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-8\left(2x^{2}-1\right)+7\left(x-1\right)\left(x+2\right)$$

-8 ga 2x^{2}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+7\left(x-1\right)\left(x+2\right)$$

7 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+\left(7x-7\right)\left(x+2\right)$$

7x-7 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-16x^{2}+8+7x^{2}+7x-14$$

-9x^{2} ni olish uchun -16x^{2} va 7x^{2} ni birlashtirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-9x^{2}+8+7x-14$$

-6 olish uchun 8 dan 14 ni ayirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}-9x^{2}-6+7x$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -9x^{2}-6+7x ni \frac{\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} marotabaga ko'paytirish.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}+\frac{\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} va \frac{\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}+\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2}}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\left(2x^{4}-2x^{3}-4x^{2}-1\right)^{2}+\left(-9x^{2}-6+7x\right)\left(x-2\right)^{2}\left(x+1\right)^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{8}-4x^{7}-8x^{6}-2x^{4}-4x^{7}+4x^{6}+8x^{5}+2x^{3}-8x^{6}+8x^{5}+16x^{4}+4x^{2}-2x^{4}+2x^{3}+4x^{2}+1-9x^{6}+18x^{5}+27x^{4}-36x^{3}-36x^{2}-6x^{4}+12x^{3}+18x^{2}-24x-24+7x^{5}-14x^{4}-21x^{3}+28x^{2}+28x}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

4x^{8}-4x^{7}-8x^{6}-2x^{4}-4x^{7}+4x^{6}+8x^{5}+2x^{3}-8x^{6}+8x^{5}+16x^{4}+4x^{2}-2x^{4}+2x^{3}+4x^{2}+1-9x^{6}+18x^{5}+27x^{4}-36x^{3}-36x^{2}-6x^{4}+12x^{3}+18x^{2}-24x-24+7x^{5}-14x^{4}-21x^{3}+28x^{2}+28x kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{8}-8x^{7}-21x^{6}+19x^{4}+41x^{5}-41x^{3}+18x^{2}-23+4x}{\left(x-2\right)^{2}\left(x+1\right)^{2}}$$

\left(x-2\right)^{2}\left(x+1\right)^{2} ni kengaytirish.

$$\frac{4x^{8}-8x^{7}-21x^{6}+19x^{4}+41x^{5}-41x^{3}+18x^{2}-23+4x}{x^{4}-2x^{3}-3x^{2}+4x+4}$$