SOLUTION: solve variable in equation {{{ (2)/(y+2)-(6)/(y^2+5y+6)=(5)/((y+2)^2)}}}

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Question 1123485: solve variable in equation
+%282%29%2F%28y%2B2%29-%286%29%2F%28y%5E2%2B5y%2B6%29=%285%29%2F%28%28y%2B2%29%5E2%29
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+%282%29%2F%28y%2B2%29-%286%29%2F%28y%5E2%2B5y%2B6%29=%285%29%2F%28%28y%2B2%29%5E2%29

+%282%29%2F%28y%2B2%29-%286%29%2F%28y%5E2%2B3y%2B2y%2B6%29=%285%29%2F%28%28y%2B2%29%5E2%29













+2y%2F%28y+%2B+3%29=5%2F%28y%2B2%29

+2y%28y+%2B+2%29=5%28y%2B3%29
+2y%5E2%2B4y+=5y%2B15
+2y%5E2%2B4y+-5y-15=0
+2y%5E2+-y-15=0
+2y%5E2+-6y%2B5y-15=0
+%282y%5E2+-6y%29%2B%285y-15%29=0
+2y%28y+-3%29%2B5%28y-3%29=0
+%28y+-+3%29+%282y+%2B+5%29+=+0
solutions:

if +%28y+-+3%29++=+0->y=3
if ++%282y+%2B+5%29+=+0->2y=-5->y=-5%2F2







Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve variable in equation
+%282%29%2F%28y%2B2%29-%286%29%2F%28y%5E2%2B5y%2B6%29=%285%29%2F%28%28y%2B2%29%5E2%29
+%282%29%2F%28y%2B2%29-%286%29%2F%28y%5E2%2B5y%2B6%29=%285%29%2F%28%28y%2B2%29%5E2%29

 ------ Factoring denominator

From this, we can see that matrix%281%2C3%2C+x+%3C%3E+-+2%2C+and%2C+x+%3C%3E+-+3%29

 -------- Multiplying by LCD, (y + 3)(y + 2)2

matrix%281%2C3%2C+2%28y%5E2+%2B+5y+%2B+6%29+-+6y+-+12%2C+%22=%22%2C+5y+%2B+15%29

matrix%281%2C3%2C+2y%5E2+%2B+10y+%2B+12+-+6y+-+12%2C+%22=%22%2C+5y+%2B+15%29

matrix%281%2C3%2C+2y%5E2+%2B+10y+-+6y+-+5y+%2B+12+-+12+-+15%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+2y%5E2+-+y+-+15%2C+%22=%22%2C+0%29

(2y + 5)(y - 3) = 0 ------ Factoring TRINOMIAL

2y + 5 = 0       OR         y - 3 = 0

Solving for y above gives you:  <======= These values are NOT part of the restricted values of x.