3x+54/6x^{2+3x}+4x^2+9/4x^2-1=x+3/2/3x-frac{8}{3}*frac{x^2}{(1-4x^2)} eching

$$\frac { 3 x + 54 } { 6 x ^ { 2 } + 3 x } + \frac { 4 x ^ { 2 } + 9 } { 4 x ^ { 2 } - 1 } = \frac { x + \frac { 3 } { 2 } } { 3 x } - \frac { 8 } { 3 } \cdot \frac { x ^ { 2 } } { ( 1 - 4 x ^ { 2 } ) }$$

x uchun yechish

$$x=\frac{15}{38}\approx 0,394736842$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{1}{2},0,\frac{1}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x\left(2x-1\right)\left(2x+1\right) ga, 6x^{2}+3x,4x^{2}-1,3x,3,1-4x^{2} ning eng kichik karralisiga ko‘paytiring.

$$\left(2x-1\right)\left(3x+54\right)+3x\left(4x^{2}+9\right)=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

2x-1 ga 3x+54 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6x^{2}+105x-54+3x\left(4x^{2}+9\right)=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

3x ga 4x^{2}+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+105x-54+12x^{3}+27x=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

132x ni olish uchun 105x va 27x ni birlashtirish.

$$6x^{2}+132x-54+12x^{3}=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$6x^{2}+132x-54+12x^{3}=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)x^{3}$$

4x^{2}-1 ga x+\frac{3}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+132x-54+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}-\frac{8}{3}\left(-3\right)x^{3}$$

-8 hosil qilish uchun \frac{8}{3} va -3 ni ko'paytirish.

$$6x^{2}+132x-54+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}-\left(-8x^{3}\right)$$

-8x^{3} ning teskarisi 8x^{3} ga teng.

$$6x^{2}+132x-54+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}+8x^{3}$$

12x^{3} ni olish uchun 4x^{3} va 8x^{3} ni birlashtirish.

$$6x^{2}+132x-54+12x^{3}=12x^{3}+6x^{2}-x-\frac{3}{2}$$

Ikkala tarafdan 12x^{3} ni ayirish.

$$6x^{2}+132x-54+12x^{3}-12x^{3}=6x^{2}-x-\frac{3}{2}$$

0 ni olish uchun 12x^{3} va -12x^{3} ni birlashtirish.

$$6x^{2}+132x-54=6x^{2}-x-\frac{3}{2}$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$6x^{2}+132x-54-6x^{2}=-x-\frac{3}{2}$$

0 ni olish uchun 6x^{2} va -6x^{2} ni birlashtirish.

$$132x-54=-x-\frac{3}{2}$$

x ni ikki tarafga qo’shing.

$$132x-54+x=-\frac{3}{2}$$

133x ni olish uchun 132x va x ni birlashtirish.

$$133x-54=-\frac{3}{2}$$

54 ni ikki tarafga qo’shing.

$$133x=-\frac{3}{2}+54$$

\frac{105}{2} olish uchun -\frac{3}{2} va 54'ni qo'shing.

$$133x=\frac{105}{2}$$

Ikki tarafini 133 ga bo‘ling.

$$x=\frac{\frac{105}{2}}{133}$$

\frac{\frac{105}{2}}{133} ni yagona kasrga aylantiring.

$$x=\frac{105}{2\times 133}$$

266 hosil qilish uchun 2 va 133 ni ko'paytirish.

$$x=\frac{105}{266}$$

\frac{105}{266} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{15}{38}$$