Question

What is the sum?
4x+1/x+2 + x-1/3x

Answer 1

Answer: c

Step-by-step explanation:

Answer 2

C.
`(13^(2) + 4x - 2)/(3x(x+2))`

Step-by-step explanation:

Since both fractions don't have the same denominator, we have to make them with the same denominator before we can actually do the addition.

So, here's the initial problem:

`(4x + 1)/(x + 2) + (x - 1)/(3x)`

To make them with the same denominator, we'll multiply each side by 1, using the denominator of the other part... like this:

`(4x + 1)/(x + 2) * (3x)/(3x) + (x - 1)/(3x) * (x + 2)/(x + 2)`

Since we multiply by 1 (expressed differently, but still just 1), the numbers aren't really changed.

Then we make the multiplications, first part:

`(4x + 1)/(x + 2) * (3x)/(3x) = ((12x^(2) + 3x) )/(3x^(2) + 6)`

Now the second part:

`(x - 1)/(3x) * (x + 2)/(x + 2) = (x^(2) + x -2)/(3x^(2) + 6)`

We now have both sides of the addition with the same denominator, and we can add the numerators.

`((12x^(2) + 3x) )/(3x^(2) + 6) + (x^(2) + x -2)/(3x^(2) + 6) = (13x^(2) +4x -2)/(3 (x^(2) + 2))`

We also simplified the denominator at the end, by extracting the 3 which was common.