Question

Find the sum of the terms.



The numerator of the simplified sum is

Answer 1

4x+6: C

Explanation:

Answer 2

`4x+6` is the numerator.

Explanation:

The given term is:

`(x)/(x^(2)+3x+2 )+(3)/(x+1)`

First of all, let us have a look at the denominator of the 1st term:

`x^(2)+3x+2`

Factorizing by writing
`3x` as
`2x+x` and then taking 'x' and '1' common respectively:

`x^(2)+2x+x+2 \\\Rightarrow x(x+2)+1(x+2 )\\\Rightarrow (x+1)(x+2 )`

Now, solving the given expression by taking LCM:

`\frac{x}{(x+{2})(x+1)}+(3)/(x+1)\\\Rightarrow \frac{x+3(x+2)}{(x+{2})(x+1)}\\\Rightarrow \frac{x+3x+6}{(x+{2})(x+1)}\\\Rightarrow \frac{4x+6}{(x+{2})(x+1)}`

Any expression
`(p)/(q)` has
`p` as its numerator and
`q` as its denominator.

So, the numerator of simplified term is:

`4x+6`