F(x)=5x^2-(x+7/x^3-x eching

$$F ( x ) = \frac { 5 x ^ { 2 } - ( x + 7 } { x ^ { 3 } - x }$$

F uchun yechish

$$F=-\frac{7+x+5x^{3}-5x^{5}}{x^{2}\left(x^{2}-1\right)}$$

$$x\neq 0\text{ and }|x|\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x\left(x-1\right)\left(x+1\right) ga ko'paytirish.

$$Fxx\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$Fx^{2}\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

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

$$\left(Fx^{3}-Fx^{2}\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

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

$$Fx^{4}-Fx^{2}=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

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

$$Fx^{4}-Fx^{2}=5x^{3}\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

5x^{3} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Fx^{4}-Fx^{2}=\left(5x^{4}-5x^{3}\right)\left(x+1\right)-\left(x+7\right)$$

5x^{4}-5x^{3} ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-\left(x+7\right)$$

x+7 teskarisini topish uchun har birining teskarisini toping.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-x-7$$

F'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{4}-x^{2}\right)F=5x^{5}-5x^{3}-x-7$$

Ikki tarafini x^{4}-x^{2} ga bo‘ling.

$$\frac{\left(x^{4}-x^{2}\right)F}{x^{4}-x^{2}}=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

x^{4}-x^{2} ga bo'lish x^{4}-x^{2} ga ko'paytirishni bekor qiladi.

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

5x^{5}-5x^{3}-x-7 ni x^{4}-x^{2} ga bo'lish.

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{2}\left(x^{2}-1\right)}$$