solve using LCD 3X/8+4/X+1=50/2X+2?

Answer 1

Parentheses are key here.
3x/8 + 4/(x+1) = 50/(2x+2)

Notice that 2x+2 factors into 2(x+1).
Multiply every term by 8(x+1)

3x(x+1) + 4(8) = 50(4)
3x^2 + 3x + 32 = 200
3x^2 + 3x - 168 = 0
Divide both sides by 3
x^2 + x - 56 = 0
Factor.
(x+8)(x-7) = 0
x+8 = 0 or x-7 = 0
x = -8 or x = 7

Remember to check your answers.

Answer 2

3x / 8 + 4 / (x + 1) = 50 / 2(x + 1)
3x + 32 / (x + 1) = 200 / (x + 1)
3x (x + 1) + 32 = 200
3x² + 3x - 168 = 0
x² + x - 56 = 0
(x + 8) (x - 7) = 0
x = - 8 , x = 7