Noldan farqli haqiqiy $a,b$ sonlari uchun $a\ne b$ bo‘lsin. $a\cdot\dfrac{(a^2b^{-1}-a^{-1}b^2)^{-1}}{\left(\dfrac{a}{b}+1+\dfrac{b}{a}\right)^{-1}}-\dfrac{b}{a-b}$ ni soddalashtiring.
- A. $0$
- B. $a-b$
- C. $1$
- D. $-1$
Algebraik kasrlar bo‘yicha savol
Javob va yechimni ko‘rish
Javob: $1$
Katta kasr $\dfrac{ab}{a^3-b^3}\cdot\dfrac{a^2+ab+b^2}{ab}=\dfrac{1}{a-b}$ ga teng. Shuning uchun butun ifoda $\dfrac{a-b}{a-b}=1$.
Mavzuni mustahkamlang
Bu savol Algebraik kasrlar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganishShu mavzudagi boshqa savollar
Ifodani soddalashtiring: $\frac{x^2 - 9}{x^2 + 6x + 9} \cdot \frac{x + 3}{x - 3}$Kasrlarni ayiring: $\frac{2a}{a^2 - b^2} - \frac{1}{a - b}$Tenglamani yeching: $\frac{x}{x-2} - \frac{2}{x-2} = 1$Ifodani soddalashtiring: $\left(\frac{1}{x} + \frac{1}{y}\right) : \frac{x^2 - y^2}{xy}$Agar $x + \frac{1}{x} = 5$ bo'lsa, $x^2 + \frac{1}{x^2}$ ning qiymatini toping.