Question

if (a³ + 3ab²) / (3a²b + b³) = (x³ + 3xy²) / (3x²y + y³), then

1. ax = by

2. xy = ab

3. ay = bx

4. ax = b

Answer 1

(a³ +3ab²)/(3a²b+b³) = (x³ +3xy²)/(3x²y+y³)

add both sides 1

(a³ +3ab²+3a²b+b³)/(3a²b+b³) =(x³+3xy²+3x²y+y³)/(3x²y+y³)

(a + b)³/(3a²b+b³) =(x +y)³/(3x²y+y³)


(a/b +1)³/(3a/b +1) = (x/y+1)³/(3x/y+1)

here you can see that both sides just like same only when
a/b = x/y

so,

ay = bx is the answer option (3)