math question!!?

Question

(y^2+2y+2 / y+1)+(y^2+8y+20 / y+4) = (y^2+4y+6 / y+2)+ (y^2+6y+12 / y+3)
~~~p.s. y^2 means : y x y ~~~~
y=?

i think it can be answered.i did that question before,but i forget how to solve it.

sorry,i meant [(y^2 + 2y +2)/(y + 1)].......

debarun p: how did you solve it?

Answer 1

(2y³+15y²+38y+28)/(y²+5y+4) = (2y³+15y²+42y+42)/(y²+5y+6)
2y^5 + 25y^4 + 125y³ + 308y² + 368y + 168 = 2y^5 + 25y^4 + 125y³ + 312y² + 378y +168
Making it a quintic equation, isolate all y's to one side to equate it to 0. But when you have done this, you will get:
-4y² - 10y = 0
Notice that it became a quadratic equation. Factoring this, we get:
-2y (2y + 5) = 0
-2y = 0 OR 2y+5=0
y=0 OR y= -5/2
By substitution, -5/2 or 0 make the equation true.
The solution set is: {-5/2, 0}.

Answer 2

When you say 2 / y+1, for instance, do you mean (2/y) +1 or
2/(y+1)?

If (2/y) + 1, then combine terms:
2y^2 + 10y + (22/y) + 5 = 2y^2 + 10y + (18/y) + 5
All terms cancel except 22/y = 18/y, which has no solution (y=0 is undefined)

If 2/(y+1), then the first 2 terms still cancel:
2y^2+10y+2/(y+1)+20/(y+4) = 2y^2+10y+6/(y+2)+12/(y+3)
Simplify to 2/(y+1) + 20/(y+4) = 6/(y+2) + 12/(y+3)
Multiply every term by (y+1)(y+2)(y+3)(y+4) to eliminate fractions
Then simplify and solve the 3rd degree polynomial:
y = -2.5, 0, or 1

Answer 3

Intriguing!
Try:
((y+2)(y+1)-y)/(y+1) + ((y+4)(y+5)-y)/(y+4)
=((y+2)(y+3)-y)/(y+2)+((y+3)(y+4)-y)/(y+3)

y+2-y/(y+1)+y+5-y/(y+4) = y+3-y/(y+2)+y+4-y/(y+3)

1/(y+1)+1/y+4)=1/(y+2)+1/(y+3)

(y+2)(y+3)(y+4)+(y+1)(y+2)(y+3) = (y+1)(y+3)(y+4)+(y+1)(y+2)(y+4)

(y+2)(y+4)(y+3-y-1) = (y+1)(y+3)(y+4-y-2)

y^2+6y+8 = y^2+4y+3

6y-4y = 3-8

2y = -5

y=-5/2

(25/4-5+2)/(-3/2)+(25/4-20+20)(/(3/2)=(25/4-10+6)/(-1/2)+(25/4-15+12)/(1/2)

-(25-12)/3+25/3=-(25-16)+25-12

4=4

and very tedious!

Answer 4

y=0 and -2.5

okay I thought you meant (y^2 + 2y +2)/(y + 1) etc.

but you wrote y^2 + 2y + 2/y + 1 etc.

in which case their is no finite answer because it simplifies to
11/y = 9/y

Answer 5

Looks like a complex answer, since the numerators can't be easily factorized

Answer 6

It can't be answered.

I forgot what it's called when a question can't be answered. But the two sides don't equal so yeah.

Answer 7

4 answers

y=+infinity, y = -infinity, y = -9.464..., y = -2.535...

where the numerical answers are approximations.