320 Вправа 320Алгебра 8 клас Бевз 2025 · § 7 · стор. 67

320. Find the value of the expression ((a + x)/a − (x − 1)/x) · a²x/(x⁴ − a²), if a = 2,25, x = 3,5.

1) ${\displaystyle \frac{{a+x}^{\mathrm{\setminus }x}}{a}-\frac{{x-1}^{\mathrm{\setminus }a}}{x}=}$${\displaystyle \frac{x(a+x)-a(x-1)}{ax}}$=

=${\displaystyle \frac{ax+x^2-ax+a}{ax}=}$${\displaystyle \frac{x^2+a}{ax}}$;

2) ${\displaystyle \frac{x^2+a}{ax}\cdot \frac{a^{2}x}{x^4-a^2}=}$${\displaystyle \frac{(x^2+a)\cdot a^{2}x}{ax\cdot (x^4-a^2)}}$=

=${\displaystyle \frac{\cancel{x}\cancel{a}a\cancel{\left(x^2+a\right)}}{\cancel{x}\cancel{a}\cancel{\left(x^2+a\right)}(x^2-a)}=}$${\displaystyle \frac{a}{x^2-a}}$;

if a = 2,25, x = 3,5, then ${\displaystyle \frac{2,25}{3,5^2-2,25}}$=

=${\displaystyle \frac{2,25}{12,25-2,25}=}$${\displaystyle \frac{2,25}{10}=}$${\displaystyle 0,225}$.