Question

Determine os quocientes e quando possível simplifiqueos :
urgentee

Answer 1

a) 2x²/5a : x/15a =

2x²/5a · 15a/x =

30x²a/5ax = 6x

b) x²y/m³n : xy²/m²n =

x²y/m³n . m²n/xy² =

x²ym²n/m³nxy² = x/ym  

c) 5p⁵q/2a⁴ : 25p⁴q/2a⁵ =

5p⁵q/2a⁴ . 2a⁵/25p⁴q =

10p⁵a⁵/50a⁴p⁴q = pa/5q  

d) 21t⁴/12b : 7t⁵b/2 =

21t⁴/12b . 2/7t⁵b =

42t⁴/84t⁵b² = 1/2tb²  

e) 12a²/8xy : 6/axy =

12a²/8xy . axy/6 =

12a³xy/48xy = a³/4  

f) x/(a - 1) : x²/(a² - 1) =

x/(a - 1) . (a² - 1)/x² =

x(a² - 1)/x²(a - 1) =

x(a + 1)(a - 1)/x²(a - 1)  = (a + 1)/x  

g) (a + b)/(a² - b²) : a/(a² - ab) =

(a + b)/(a² - b²) . (a² - ab)/a =  

(a + b)(a² - ab)/a(a + b)(a - b) =

(a² - ab)/a(a - b) =

(a² - ab)/(a² - ab) = 1  

h) 2y⁴/(3a⁵ + 9a⁴) : 6y³/(3a + 9) =

2y⁴/(3a⁵ + 9a⁴) . (3a + 9)/6y³ =

2y⁴(3a + 9)/6y³(3a⁵ + 9a⁴) =

2y⁴(3a + 9)/6y³[a⁴(3a + 9)] = y/3a⁴  

i) (a² - 2a + 1)/x² : (a² - 1)/x =

(a² - 2a + 1)/x² . x/(a² - 1) =  

(a - 1)(a - 1)/x² . a/(a + 1)(a - 1) =

a(a - 1)(a - 1)/x²(a + 1)(a - 1) = a(a - 1)/x²(a + 1)  

j) (t - 2)/(5p + 25) : (2t - 4)/(p² - 25) =

(t - 2)/(5p + 25) . (p² - 25)/(2t - 4) =  

(t - 2)(p² - 25)/(5p + 25)(2t - 4) =

(t - 2)(p + 5)(p - 5)/5(p + 5).2(t - 2) =  

(p - 5)/5.2 = (p - 5)/10