4 - 3/(x+1) = 5/ (x+2) find all answers for x?

Answer 1

First: eliminate fractions - multiply the denominator with each term.

(x+1)(x+2)(4)-(x+1)(x+2)[3/(x+1)]=(x+1)(x+2)[5/(x+2)]

Sec: cross cancel "like" terms & combine the rest.

(x+1)(x+2)(4)-(x+2)(3)=(x+1)(5)
(x^2+2x+x+2)(4)-(3x+6)=5x+5
(x^2+3x+2)(4)-3x-6=5x+5
4x^2+12x+8-3x-6=5x+5

*Set the equation to "0" > subtract 5x & subtract 5 from both sides (when you move a term to the opposite side, always use the opposite sign).

4x^2+12x+8-3x-6-5x-5=5x-5x+5-5
4x^2+4x-3 = 0

Third: factor the expression & you should get...

(2x+3)(2x-1) = 0

Now, set both parenthesis to "0" & solve the "x" variables.

a. 2x+3 = 0
2x+3-3 = 0-3
2x = - 3
2x/2 = -3/2
x = -3/2

b. 2x-1 = 0
2x-1+1=0+1
2x = 1
2x/2 = 1/2
x = 1/2

Solutions: 1/2, -3/2

Answer 2

4(x + 1).(x + 2) - 3.(x + 2) = 5.(x + 1)
4.(x² + 3x + 2) - 3x - 6 = 5x + 5
4x² + 12x + 8 - 8x - 11 = 0
4x² + 4x - 3 = 0
(2x + 3).(2x - 1) = 0
x = - 3/2 , x = 1/2

Answer 3

4 - [(3)/(x + 1)] = 5/(x + 2)
[4(x + 1)]/(x + 1) - 3/(x + 1) = 5/(x + 2)
[4(x + 1) - 3]/(x + 1) = 5/(x + 2)
(4x + 4 - 3)/(x + 1) = 5/(x + 2)
4(x + 1)/(x + 1) = 5/(x + 2)
4 = 5/(x + 2)
4(x + 2) = 5
4x + 8 = 5
4x = 5 - 8
4x = -3
x = -3/4