Answer:
5/(y+5)
Step-by-step explanation:
Perhaps you want the sum ...
[tex]\dfrac{3y}{y^2+7y+10}+\dfrac{2}{y+2}\\\\=\dfrac{3y}{(y+2)(y+5)}+\dfrac{2(y+5)}{(y+2)(y+5)}=\dfrac{3y+2(y+5)}{(y+2)(y+5)}\\\\=\dfrac{5y+10}{(y+2)(y+5)}=\dfrac{5(y+2)}{(y+2)(y+5)}=\boxed{\dfrac{5}{y+5}}[/tex]
_____
Comment on rational expressions
When writing ratios in plain text, it is imperative to put parentheses around numerators and denominators. (If the numerator is a product only, then parentheses are optional.)
Your expression might be properly written as ...
3y/(y^2 +7y +10) +2/(y+2)
As you have written it, it simplifies to ...
3(y/y)2 +7y +10 +2/y +2 = 3·2 +7y +2/y +12
= 7y +2/y +18
Please note, too, the exponentiation symbol (^).
