Question

Add fractions q/q2 + 5q +6 and 1/q2 + 3q + 2

Answer 1

Answer is c I'm pretty sure

Answer 2

Hence, option C is correct.

Explanation:

We are asked to add two fractions:

`(q)/(q^2+5q+6)` and
`(1)/(q^2+3q+2)`

i.e.

`(q)/(q^2+5q+6)+(1)/(q^2+3q+2)`

We know that:

`q^2+5q+6` could also be written as:

`q^2+5q+6=q^2+3q+2q+6\\\\=q(q+3)+2(q+3)\\\\=(q+2)(q+3)`

Similarly
`q^2+3q+2` could also be written aS:

`q^2+3q+2=q^2+2q+q+2\\\\=q(q+2)+1(q+2)\\\\\=(q+1)(q+2)`

Hence we have to add:

`(q)/((q+2)(q+3))+(1)/((q+1)(q+2))\\\\\\=(q* (q+1)+1* (q+3))/((q+1)(q+2)(q+3))\\\\\\=(q^2+q+q+3)/((q+1)(q+2)(q+3))\\\\\\=(q^2+2q+3)/((q+1)(q+2)(q+3))`

Hence, Option C is correct.