What is the simplified form of the quantity 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 ?

a 3y times the quantity 2x plus 1 over x times the quantity x plus 2
b x times the quantity x plus 2 over 3y times the quantity 2x plus 1
c x times the quantity x minus 2 over 3y times the quantity 2x minus 1
d 3y times the quantity 2x minus 1 over x times the quantity x minus 2

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

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b.

step-by-step explanation: