Very difficult Algebra 2 problem. Appreciate the help?

Question

this problem has been bugging me for the last 25 minutes


Solve. If no solution exists say NO SOLUTION

10/y^2 - 4 = 1 - 1/y + 2

appreciate the help

ya sorry its 1/(y+2)

Answer 1

10/y^2 - 4 = 1 - 1/(y + 2 ) ?

It's hard to read your question.
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I guess it is

10/(y^2-4) = 1 - 1/(y+2)

If it is true, then
10/[(y+2)(y-2)] = (y+1)/(y+2)

Multiply by (y+2),
10/(y-2) = y+1
which is equivalent to
10 = y^2-y-2
y^2-y-12 = (y+3)(y-4) = 0

y = -3, or 4

Answer 2

If I am reading this right it is

10/(y^2-4) = 1 - 1/(y+2)

Factor the y^2-4 into (y+2)(y-2) and mutiply both sides by (y+2)(y-2) which is the least common denominator

[10(y+2)(y-2)/(y+2)(y-2)] = 1*(y+2)(y-2) - [1(y+2)(y-2)/(y+2)]

Now cancel where you can and this simplifies to

10 = (y+2)(y-2) - (y-2)
10 = y^2 - 4 - y + 2
10 = y^2 - y - 2
y^2 - y - 12 = 0
(y+3)(y-4) = 0
y = -3, 4

** be sure to check that your solutions are within the domain of the problem!!

Answer 3

10 / (y^2 - 4) = 1 - 1/(y+2) ==> Multiply both sides by y+2, noting that (y^2 - 4) = (y+2)(y-2)
10 / (y-2) = y+2-1 = y+1 ==> Multiply both sides by y-2
10 = (y+1)(y-2) = y^2 - y - 2
0 = y^2 - y - 12
0 = (y+3)(y-4)
y = -3 or y = 4

Answer 4

10/y^2 - 4 = 1 - 1/y + 2
Multiplying both sides by y^2
10 - 4y^2 = y^2 - y + 2y^2
0 = - 10 + 4y^2 + y^2 - y + 2y^2 = 7y^2 - y - 10
7y^2 - y - 10 = 0
y = [1 +- sqrt{1^2 - 4(7)(-10)}] / [2(7)]
y = [1 +- sqrt281] / 14 = [1 +- 16.8] / 14
y = 1.27 and y = 1.13

Answer 5

10/(y-2)(y+2)=1- 1/(y+2)
10/(y-2)= (y+2) -1
10/(y-2)=(y+1)
10=(y+1)(y-2)
10=y^2-y-2
0=y^2-y-12
0=(y-4)(y+3)
y=4 or -3

Answer 6

add 4 to both sides

10/y^2=7+1/y

subtract 1/y from both sides

10/y^2-1/y=7

multiply 1/y by y/y

10/y^2-y/y^2=7

combine fractions

(10-y)/y^2=7

multiply both sides by y^2

10-y=7y^2

rearrange

7y^2+y-10=0

use quadratic formula

y=(-1+/-(1+280)^.5)/14

solve the rest yourself :-)


I think i ready your problem wrong though, you really need to use parenthesis

Answer 7

Your question is ambiguous. Please use parentheses to eliminate ambiguity and restate it so we can answer.