Question

Find the sum of the terms. The numerator of the simplified sum is

Answer 1

Answer:

$4x+6$ is the numerator.

Step-by-step explanation:

The given term is:

$\dfrac{x}{x^{2}+3x+2 }+\dfrac{3}{x+1}$

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:

$\dfrac{x}{(x+{2})(x+1)}+\dfrac{3}{x+1}\\\Rightarrow \dfrac{x+3(x+2)}{(x+{2})(x+1)}\\\Rightarrow \dfrac{x+3x+6}{(x+{2})(x+1)}\\\Rightarrow \dfrac{4x+6}{(x+{2})(x+1)}$

Any expression $\frac{p}{q}$ has $p$ as its numerator and $q$ as its denominator.

So, the numerator of simplified term is:

$4x+6$