For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = \frac { x ^ { 2 } + 4 x + 4 } { x ^ { 2 } + 5 x + 6 } , g ( x ) = \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 7 x + 10 }$$
A) $\frac { x ^ { 2 } + 3 x } { x + 5 }$
B) $\frac { x } { x + 5 }$
C) $\frac { x } { x ^ { 2 } + 5 x + 6 }$
D) $\frac { 1 } { x + 5 }$

Question

Quizplus · Accepted Answer

To find f(x) ∙ g(x), multiply the two functions together:
f(x) ∙ g(x) = [ ( x^2 + 4x + 4 ) / ( x^2 + 5x + 6 ) ] ∙ [ ( x^2 + 3x ) / ( x^2 + 7x + 10 ) ]
Simplify both numerators and denominators before multiplying:
f(x) ∙ g(x) = [(x + 2)(x + 2) / (x + 2)(x + 3) ] ∙ [ x(x + 3) / (x + 2)(x + 5) ]
Cancel out common factors:
f(x) ∙ g(x) = [ ( x + 2 ) / ( x + 3 ) ] ∙ [ x / ( x + 5 ) ]
f(x) ∙ g(x) = ( x / ( x + 3 ) ) ∙ ( x + 2 ) / ( x + 5 )
f(x) ∙ g(x) = x(x + 2) / ( x + 3 ) ( x + 5 )
Simplify the expression: 
f(x) ∙ g(x) = x(x + 2) / ( x^2 + 8x + 15 )
f(x) ∙ g(x) = x(x + 2) / ( x + 5 ) ( x + 3 )
Therefore, the answer is B, which is ( x / ( x + 5 ) ) ( x + 2 ) / ( x + 3 ).

For the Given Functions F(x) and G(x), Find F(x) ∙ f(x)=x2+4x+4x2+5x+6,g(x)=x2+3xx2+7x+10f ( x ) = \frac { x ^ { 2 } + 4 x + 4 } { x ^ { 2 } + 5 x + 6 } , g ( x ) = \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 7 x + 10 }f(x)=x2+5x+6x2+4x+4​,g(x)=x2+7x+10x2+3x​

For the Given Functions F(x) and G(x), Find F(x) ∙ $f ( x ) = \frac { x ^ { 2 } + 4 x + 4 } { x ^ { 2 } + 5 x + 6 } , g ( x ) = \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 7 x + 10 }$