Question

What is the simplified form of the quantity x squared plus 5x plus 6 over 15 x y squared all over the quantity 2x squared plus 7x plus 3 over 5 x squared y ?

3y times the quantity 2x plus 1 over x times the quantity x plus 2
x times the quantity x plus 2 over 3y times the quantity 2x plus 1
x times the quantity x minus 2 over 3y times the quantity 2x minus 1
3y times the quantity 2x minus 1 over x times the quantity x minus 2

Answer 1

x² + 5 x + 6 = x² + 2 x + 3 x + 6 = x ( x + 2 ) + 3 ( x + 2 ) = ( x + 3 ) ( x + 2 )
2 x² + 7 x + 3 = 2 x² + 6 x + x + 3 = 2 x ( x + 3 ) + ( x + 3) = ( 2 x +1 ) ( x + 3 )
(x+2)(x+3)/ 15 x y² : ( x+3 ) ( 2 x + 1 ) / 5 x² y =

`(( x +2 ) ( x + 3 ) )/(15xy ^(2) ) * (5 x^(2) y)/((2x+1)(x+3)) = \\ =(x(x+2))/(3y(2x+1) )`
Answer:
B ) x times the quantity of x plus 2 over 3 y times the quantity 2 x plus 1