Question

What is the sum? 3 y / Y 2 + 7 y + 10 + 2 / y + 2​

Answer 1

Answer:

  5/(y+5)

Step-by-step explanation:

Perhaps you want the sum ...

  $\dfrac{3y}{y^2+7y+10}+\dfrac{2}{y+2}\\\\=\dfrac{3y}{(y+2)(y+5)}+\dfrac{2(y+5)}{(y+2)(y+5)}=\dfrac{3y+2(y+5)}{(y+2)(y+5)}\\\\=\dfrac{5y+10}{(y+2)(y+5)}=\dfrac{5(y+2)}{(y+2)(y+5)}=\boxed{\dfrac{5}{y+5}}$

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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 (^).