Answer:
Hence, option C is correct.
Step-by-step explanation:
We are asked to add two fractions:
[tex]\dfrac{q}{q^2+5q+6}[/tex] and [tex]\dfrac{1}{q^2+3q+2}[/tex]
i.e.
[tex]\dfrac{q}{q^2+5q+6}+\dfrac{1}{q^2+3q+2}[/tex]
We know that:
[tex]q^2+5q+6[/tex] could also be written as:
[tex]q^2+5q+6=q^2+3q+2q+6\\\\=q(q+3)+2(q+3)\\\\=(q+2)(q+3)[/tex]
Similarly [tex]q^2+3q+2[/tex] could also be written aS:
[tex]q^2+3q+2=q^2+2q+q+2\\\\=q(q+2)+1(q+2)\\\\\=(q+1)(q+2)[/tex]
Hence we have to add:
[tex]\dfrac{q}{(q+2)(q+3)}+\dfrac{1}{(q+1)(q+2)}\\\\\\=\dfrac{q\times (q+1)+1\times (q+3)}{(q+1)(q+2)(q+3)}\\\\\\=\dfrac{q^2+q+q+3}{(q+1)(q+2)(q+3)}\\\\\\=\dfrac{q^2+2q+3}{(q+1)(q+2)(q+3)}[/tex]
Hence, Option C is correct.
