Answer:
[tex]4x+6[/tex] is the numerator.
Step-by-step explanation:
The given term is:
[tex]\dfrac{x}{x^{2}+3x+2 }+\dfrac{3}{x+1}[/tex]
First of all, let us have a look at the denominator of the 1st term:
[tex]x^{2}+3x+2[/tex]
Factorizing by writing [tex]3x[/tex] as [tex]2x+x[/tex] and then taking 'x' and '1' common respectively:
[tex]x^{2}+2x+x+2 \\\Rightarrow x(x+2)+1(x+2 )\\\Rightarrow (x+1)(x+2 )[/tex]
Now, solving the given expression by taking LCM:
[tex]\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)}[/tex]
Any expression [tex]\frac{p}{q}[/tex] has [tex]p[/tex] as its numerator and [tex]q[/tex] as its denominator.
So, the numerator of simplified term is:
[tex]4x+6[/tex]
