Which expression is equal to 3x/x+3 + x+2/x ? 4x^2-5x+6/x(x+3) x^2+8x+6/x(x+3)3x^2+6x+6/x(x+3)4x^2+5x+6/x(x+3)

Answer:D)  The given expression [tex](\frac{3x}{x+ 3})   + (\frac{x+2}{x}) = \frac{4x^{2}   + 5x + 6}{(x+3)(x)}[/tex]Step-by-step explanation:Here, the given expression is : [tex](\frac{3x}{x+ 3})   + (\frac{x+2}{x})[/tex]Let us simplify the given expression be taking LCM of the denominator and making a common base denominator.We get : [tex](\frac{3x}{x+ 3})   + (\frac{x+2}{x})  = \frac{3x(x)  + (x+2)(x+3)}{(x+3)(x)} \\\implies\frac{3x^{2}  +   (x+2)(x+3)}{(x+3)(x)}[/tex]Solving [tex](x+2) (x+3) = x^{2}  + 2x + 3x + (2)(3)  = x^{2}  + 5x + 6[/tex]Now, substitute the above value into the given expression : [tex]\frac{3x^{2}  +   (x+2)(x+3)}{(x+3)(x)} \implies\frac{3x^{2}  +   x^{2}  + 5x + 6}{(x+3)(x)}\\= \frac{4x^{2}   + 5x + 6}{(x+3)(x)}[/tex]Hence, the given expression [tex](\frac{3x}{x+ 3})   + (\frac{x+2}{x}) = \frac{4x^{2}   + 5x + 6}{(x+3)(x)}[/tex]