Question

What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction

Answer 1

its c

Explanation:

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Answer 2

`(5)/(y+5)`

Explanation:

Here, we have to find the sum of 2 fractions:

1st fraction:
`(3y)/(y^(2)+7y+10)`

2nd fraction:
`(2)/(y+2)`

Considering the denominator of 1st fraction:

`y^(2)+7y+10`

Using factorization method:

`7y` can be written as
`(2y + 5y)`.

`\Rightarrow y^(2)+2y+5y+10`

Taking 5 common from
`5y+10` and y common from
`y^(2)+2y`:
`\Rightarrow y(y+2)+5(y+2)`

Now taking
`(y+2)` common:

`\Rightarrow (y+5)(y+2)`

`(3y)/(y^(2)+7y+10)` can be written as
`(3y)/((y+5)(y+2))`

Now, calculating the sum:

`(2y)/((y+5)(y+2)) + (2)/(y+2)`

Taking LCM and solving:

`\Rightarrow (3y+2(y+5))/((y+5)(y+2))\\\Rightarrow (5y+10)/((y+5)(y+2))\\\Rightarrow (5(y+2))/((y+5)(y+2))\\\Rightarrow (5)/((y+5))`

Hence, answer is
`(5)/(y+5)`.