Solve this equation..?

Question

Solve 3/(y-1)^2 + 3/2(y-1)^2 = 2

Answer 1

answer is 5/2.

1) multiply bth sides by (y-1)^2
the eqn now is 3 + 3/2= 2(y-1)^2

2) which means 9/2= 2(y-1)^2

3) 9/4= (y-1)^2

4) Square root of both sides... 3/2= y-1

5) thus 3/2+1 = y

or 5/2 =y

done ;)

Answer 2

y=1/3 or y=5/3

Answer 3

3/(y - 1)² + 3/[2(y - 1)²] = 2

Multiply both sides by 2(y - 1)²
6 + 3 = 4(y - 1)²

Simplify
4(y - 1)² = 9

Transpose
4(y - 1)² - 9 = 0

Factor the difference of 2 squares,
[2(y - 1) + 3][2(y - 1) - 3] = 0

Simplify inside-bracket expressions
(2y + 1)(2y - 5) = 0

Thus,
2y + 1 = 0 or 2y - 5 = 0

Or simply
y = -1/2 or y = 5/2

Either solution is valid. The solution set for y is {-1/2, 5/2}

^_^

Answer 4

Multiply both sides by (y-1)^2. Then simplify, take the square root and move the one across. Your steps should look like:

3+3/2 = 2(y-1)^2
9/2 = 2(y-1)^2
9/4=(y-1)^2

y-1=+-3/2

y=1+3/2, y=1-3/2

y=5/2, -1/2

Answer 5

3/(y - 1)² + 3/(Y - 1)² = 2

2[3/(y-1)²] + 2[3(y - 1)²] = 2(2)

6/(y -1)² + 3/(y - 1)² = 4

9/Y - 1)² = 4

(Y - 1)²9/(Y - 1)² = 4(y - 1)²

9 = 4(y - 1)²

9/4 = 4(Y - 1)²/4

9/4 = (y - 1)²

√9/4 = (y - 1)²

3/2 ± = y - 1

3/2 ± 1 = y - 1 + 1

3/2 ± 1 = y

- - - - - - - - - - - - - -s

solving for negative ( - ) y

3/2 - 1 =y
3/2 - 2/2 = y

1/2 = y

- - - - - - - - - - - - - - - - -

Solving for Positive ( + ) y

3/2 + 1 = y

3/2 + 2/2 = y

5/2 = y

- - - - - - - - -s

Answer 6

let 1/(y-1)^2 = x
the equn becomes 3x+3x/2 = 2
simplifyin 9x/2 =2
so x = 4/9
so 1/(y-1)^2 = 4/9
so (y-1)^2 = 9/4
taking sq root of both the sides (y-1) = +3/2 and -3/2
so y = 1+3/2 = 5/2
or 1-3/2 = -1/2