(a^3+8):(a^2-4)=x:(a-2) eching

$$( a ^ { 3 } + 8 ) : ( a ^ { 2 } - 4 ) = x : ( a - 2 )$$

x uchun yechish (complex solution)

$$x=a^{2}-2a+4$$

$$a\neq -2\text{ and }a\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(a-2\right)\left(a+2\right) ga, a^{2}-4,a-2 ning eng kichik karralisiga ko‘paytiring.

$$a^{3}+8=\left(a+2\right)x$$

a+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{3}+8=ax+2x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$ax+2x=a^{3}+8$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(a+2\right)x=a^{3}+8$$

Ikki tarafini a+2 ga bo‘ling.

$$\frac{\left(a+2\right)x}{a+2}=\frac{a^{3}+8}{a+2}$$

a+2 ga bo'lish a+2 ga ko'paytirishni bekor qiladi.

$$x=\frac{a^{3}+8}{a+2}$$

a^{3}+8 ni a+2 ga bo'lish.

$$x=a^{2}-2a+4$$

x uchun yechish

$$x=a^{2}-2a+4$$

$$|a|\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(a-2\right)\left(a+2\right) ga, a^{2}-4,a-2 ning eng kichik karralisiga ko‘paytiring.

$$a^{3}+8=\left(a+2\right)x$$

a+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$a^{3}+8=ax+2x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$ax+2x=a^{3}+8$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(a+2\right)x=a^{3}+8$$

Ikki tarafini a+2 ga bo‘ling.

$$\frac{\left(a+2\right)x}{a+2}=\frac{a^{3}+8}{a+2}$$

a+2 ga bo'lish a+2 ga ko'paytirishni bekor qiladi.

$$x=\frac{a^{3}+8}{a+2}$$

a^{3}+8 ni a+2 ga bo'lish.

$$x=a^{2}-2a+4$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=-\sqrt{x-3}+1\text{, }&x\neq 12\\a=\sqrt{x-3}+1\text{, }&x\neq 4\end{matrix}\right,$$

a uchun yechish

$$\left\{\begin{matrix}a=-\sqrt{x-3}+1\text{, }&x\geq 3\text{ and }x\neq 12\\a=\sqrt{x-3}+1\text{, }&x\neq 4\text{ and }x\geq 3\end{matrix}\right,$$