Y(s)/U(s)=1/s(s+1)(s+2) eching

$$\frac { Y ( s ) } { U ( s ) } = \frac { 1 } { s ( s + 1 ) ( s + 2 ) }$$

Y uchun yechish

$$Y=\frac{U}{s\left(s+1\right)\left(s+2\right)}$$

$$U\neq 0\text{ and }s\neq 0\text{ and }s\neq -1\text{ and }s\neq -2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini Us\left(s+1\right)\left(s+2\right) ga, Us,s\left(s+1\right)\left(s+2\right) ning eng kichik karralisiga ko‘paytiring.

$$\left(s+1\right)\left(s+2\right)Ys=U$$

s+1 ga s+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(s^{2}+3s+2\right)Ys=U$$

s^{2}+3s+2 ga Y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(s^{2}Y+3sY+2Y\right)s=U$$

s^{2}Y+3sY+2Y ga s ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Ys^{3}+3Ys^{2}+2Ys=U$$

Y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(s^{3}+3s^{2}+2s\right)Y=U$$

Ikki tarafini 3s^{2}+s^{3}+2s ga bo‘ling.

$$\frac{\left(s^{3}+3s^{2}+2s\right)Y}{s^{3}+3s^{2}+2s}=\frac{U}{s^{3}+3s^{2}+2s}$$

3s^{2}+s^{3}+2s ga bo'lish 3s^{2}+s^{3}+2s ga ko'paytirishni bekor qiladi.

$$Y=\frac{U}{s^{3}+3s^{2}+2s}$$

U ni 3s^{2}+s^{3}+2s ga bo'lish.

$$Y=\frac{U}{s\left(s+1\right)\left(s+2\right)}$$

U uchun yechish

$$U=Ys\left(s+1\right)\left(s+2\right)$$

$$s\neq 0\text{ and }s\neq -2\text{ and }s\neq -1\text{ and }Y\neq 0$$