Respuesta :
7x^3-56x^2 over 35x^3+42x^2 times x^2-3x-40 over 25x+30
7x^2 (x-8) (x -8)(x+5)
------------------ * -------------------
7x^2 (5x + 6) 5(5x+6)
(x+5)(x - 8)^2
= -------------------------
5(5x+6)^2
7x^2 (x-8) (x -8)(x+5)
------------------ * -------------------
7x^2 (5x + 6) 5(5x+6)
(x+5)(x - 8)^2
= -------------------------
5(5x+6)^2
( (7x^3 - 56x^2) / (35x^3 + 42x^2) ) * ( (x^2 - 3x - 40) / (25x +30) )
7x^3 - 56x^2 --> 7x^2(x - 8)
35x^3 + 42x^2 --> 7x^2(5x + 6)
x^2 - 3x - 40 --> (x-8)(x+5)
25x + 30 --> 5(5x+6)
( (7x^2(x-8)) / (7x^2(5x + 6)) ) * ( ((x-8)(x+5)) / (5(5x + 6)) )
7x^2 cancel out
( ( x - 8 ) / (5x + 6) ) * ( ((x - 8)(x + 5)) / (5(5x + 6)) )
(((x-8)^2)(x + 5)) / (5 ((5x + 6)^2))
so
(x-8)^2(x+5) over 5(5x+6)^2
7x^3 - 56x^2 --> 7x^2(x - 8)
35x^3 + 42x^2 --> 7x^2(5x + 6)
x^2 - 3x - 40 --> (x-8)(x+5)
25x + 30 --> 5(5x+6)
( (7x^2(x-8)) / (7x^2(5x + 6)) ) * ( ((x-8)(x+5)) / (5(5x + 6)) )
7x^2 cancel out
( ( x - 8 ) / (5x + 6) ) * ( ((x - 8)(x + 5)) / (5(5x + 6)) )
(((x-8)^2)(x + 5)) / (5 ((5x + 6)^2))
so
(x-8)^2(x+5) over 5(5x+6)^2