Question

Resolver el problema

40 puntos

Answer 1

(a/b)[1 - (a/x)] + (b/a)[1 - (b/x)] = 1

Ejecutamos productos.

[(a/b) - (a/b)(a/x)] + [(b/a) - (b/a)(b/x)] = 1

[(a/b) - (a²/bx)] + [(b/a) - (b²/ax)] = 1

(a/b) + (b/a) - (a²/bx) - (b²/ax) = 1

Comun denominador entre: b; a; bx; ax = abx

[a(ax) + b(bx) - a²(a) - b²(b)]/(abx) = 1

[a²x + b²x - a³ - b³]/(abx) = 1

 a²x + b²x - a³ - b³ = abx

a²x + b²x - abx = a³ + b³

x(a² - ab + b²) = a³ + b³

X = [a³ + b³]/[a² - ab  + b²]

Recordemos que:


[a³ + b³] = (a + b)(a² - ab + b²)

X = [(a + b)(a² - ab + b²)]/[(a² - ab + b²)]

Cancelo (a² - ab + b²)

X = a + b

Rta: X = a + b

 

Answer 2

Respuesta:

(a/b)[1 - (a/x)] + (b/a)[1 - (b/x)] = 1

Ejecutamos productos.

[(a/b) - (a/b)(a/x)] + [(b/a) - (b/a)(b/x)] = 1

[(a/b) - (a²/bx)] + [(b/a) - (b²/ax)] = 1

(a/b) + (b/a) - (a²/bx) - (b²/ax) = 1

Comun denominador entre: b; a; bx; ax = abx

[a(ax) + b(bx) - a²(a) - b²(b)]/(abx) = 1

[a²x + b²x - a³ - b³]/(abx) = 1

 a²x + b²x - a³ - b³ = abx

a²x + b²x - abx = a³ + b³

x(a² - ab + b²) = a³ + b³

X = [a³ + b³]/[a² - ab  + b²]

Recordemos que:

[a³ + b³] = (a + b)(a² - ab + b²)

X = [(a + b)(a² - ab + b²)]/[(a² - ab + b²)]

Cancelo (a² - ab + b²)

X = a + b

Rta: X = a + b