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

Question

asked Oct 3, 2021 193k views

2 Answers

Sherif Buzz · Answer 1 · 2021-10-10T02:24:06+0000

Answer:

(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:

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) .