Maths

Hi ! I am lop****** , feel happy to answer your question.

Q 1 : (3+4/x)(1+x)=-1

A 1 :

(3+4/x)(1+x)=-1

3x + 4/x + 7 = -1
3x + 4/x + 8 = 0
3x²+ 8x + 4 = 0
(3x+2)(x+2) = 0
3x + 2 = 0 or x + 2 = 0
3x = -2 or x = -2
x = -2 or -2/3

Answer : x = -2 or -2/3

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Q 2 : (x+1/3+4/x-1)=3

A 2 :

(x+1/3+4/x-1)=3
x - 11/3 + 4/x = 0
x²- 11x/3 + 4 = 0
(x - 11/6)²- 121/36 + 4 = 0
(x - 11/6)²+ 23/36 = 0
(x - 11/6)²- ( -23/36 ) =0
[x - 11/6 + √(-23/36)][ x - 11/6 - √(-23/36)] = 0
x = 11/6 - √(-23/36) or 11/6 + √(-23/36)
x = [ 11 - √(-23)]/6 or [ 11 + √(-23)]/6
x = [ 11 - 23i ]/6 or [ 11 + 23i ]/6

Answer : x = [ 11 - 23i ]/6 or [ 11 + 23i ]/6

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