QUESTION: Simplify (10y)/(y^2-3y-18) : (5y)/(4y-24) .
The expreession A : B is equivalent to A / B.
And, (10y)/(y^2-3y-18) = (10y)/{(y+6)}
And, (5y)/(4y-24) = (5y)/{4(y-6)}
So, (10y)/(y^2-3y-18) : (5y)/(4y-24) is equivalent to (10y)/{(y+3)(y-6)} / (5y)/{4(y-6)}
(10y)/{(y+3)(y-6)} / (5y)/{4(y-6)} = (10y)/{(y+3)(y-6)} * {4(y-6)}/(5y) ={(10y)*4(y-6)} / {(y+3)(y-6)} *(5y)}
(10y)/{(y+3)(y-6)} / (5y)/{4(y-6)} = {2*4} / (y+3)
Answer: 8/(y+3)