Answer:
A. 3y times the quantity 2x plus 1 over x times the quantity x plus 2
Step-by-step explanation:
We have; 15 x y squared over x squared plus 5x plus 6 all over the quantity 5 x squared y over 2x squared plus 7x plus 3
That is;
15xy²/(x² + 5x +6) ÷ ((5x²y/(2x²+7x+3))
We can factorize expressions;
x² + 5x +6 = (x+2)(x+3)
2x²+7x+3 =(2x+1)(x+3)
Therefore we have;
15xy²/(x+2)(x+3) ÷ (5x²y/(2x+1)(x+3))
we can multiply with the reciprocal;
15xy²/(x+2)(x+3) × ((2x+1)(x+3))/5x²y
Simplifying;
3y/(x+2) × (2x+1)/x
Multiplying the numerators and then multiplying the denominators.
We get; 3y(2x+1)/ x(x+2)
= 3y(2x+1)/ x(x+2)
The answer is therefore;
A 3y times the quantity 2x plus 1 over x times the quantity x plus 2
