Question

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 1

The correct answer is
`(4x^2+5x+6)/(x(x+3))`

Explanation:

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Answer 2

D) The given expression
`((3x)/(x+ 3))   + ((x+2)/(x)) = (4x^(2)   + 5x + 6)/((x+3)(x))`

Explanation:

Here, the given expression is :
`((3x)/(x+ 3))   + ((x+2)/(x))`

Let us simplify the given expression be taking LCM of the denominator and making a common base denominator.

We get :
`((3x)/(x+ 3))   + ((x+2)/(x))  = (3x(x)  + (x+2)(x+3))/((x+3)(x)) \\\implies(3x^(2)  +   (x+2)(x+3))/((x+3)(x))`

Solving
`(x+2) (x+3) = x^(2)  + 2x + 3x + (2)(3)  = x^(2)  + 5x + 6`

Now, substitute the above value into the given expression :

`(3x^(2)  +   (x+2)(x+3))/((x+3)(x)) \implies(3x^(2)  +   x^(2)  + 5x + 6)/((x+3)(x))\\= (4x^(2)   + 5x + 6)/((x+3)(x))`

Hence, the given expression
`((3x)/(x+ 3))   + ((x+2)/(x)) = (4x^(2)   + 5x + 6)/((x+3)(x))`