find all values of y..6- 5/(y+1)= -6/(y-3)?

Answer 1

Proportional Problem

6 - 5 / (y + 1) = - 6 / (y - 3)

1 / y + 1 = 6 / y - 3

The means are - 6(y + 1)

The extremes are 1(y - 3)

- 6(y + 1) = 1(y - 3)

- 6y - 6 = y - 3

- 6y - 6 - y = y - 3 - y

- 7y - 6 = - 3

7 y - 6 + 6 = - 3 + 6

7y = 3

7y / 7 = 3 / 7

y = 3 / 7

- - - - - - - - - s-

Answer 2

Multiply through by (y+1)(y-3) to get:
6(y^2 -2y -3) - 5(y-3) + 6(y+1) = 0.
6y^2 -12y -18 - 5y +15 +6y +6 = 0
6y^2 -11y +3 = 0. This factors into:
(3y - 1)(2y - 3) = 0, so y = 1/3 or 1.5.

Answer 3

6 - 5/(y + 1) = -6/(y - 3)

In order to get rid of all fractions, multiply everything by (y + 1)(y - 3).

6(y + 1)(y - 3) - 5(y - 3) = -6(y + 1)

Expand,

6(y^2 - 2y - 3) - 5y + 15 = -6y - 6

Expand once more,

6y^2 - 12y - 18 - 5y + 15 = -6y - 6

Combine like terms.

6y^2 -17y - 3 = -6y - 6
6y^2 - 11y + 3 = 0

Factor.

(3y - 1)(2y - 3) = 0

Solve for y by equating each factor to 0.

3y - 1 = 0
3y = 1
y = 1/3

2y - 3 = 0
2y = 3
y = 3/2

Therefore, y = {1/3, 3/2}

Answer 4

[6(y+1)/y+1] - 5/y+1 = -6/y-3

(6y+1)/(y+1) = -6/y-3

(y-3)(6y+1) = -6(y+1)

6y^2 + y-18y-3 = -6y-6

6y^2-17y-3 = -6y-6

6y^2-11y+3 = 0
(3y-1)(2y-3) = 0

y=1/3 y=1.5

steps:
1. make 6 the same denominator (y+1)
2. cross multiply
3. expand the expression
4. make the RHS to be 0
5. Simplify
6. factorise
7. solve

Answer 5

A little algebra + the quadratic formula gave me
y = 11/12 ±7/12 = 1.5, 1/3

Answer 6

6-5/(y+1=-6/)y-3
6y-18-5y+15=6y-6
-5y=-3
y=3/5