Question

solve for x : x/x+1+x-1/x=4

Answer 1

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

[x.x + (x-1)(x+1)]/x(x+1) = 4

(x² + x² - 1)/x(x+1) = 4

2x² -1 = 4x(x+1)

2x² - 1 = 4x² + 4x

2x² - 4x² - 4x = 1

-2x² - 4x = 1

2x² + 4x + 1 = 0

x = -b/2a + - [√(b² - 4ac)]/2a

x = -4/2×2 + - [√(4² - 4×2×1)]/2×2

x = -1 + - [(√8)/4]

x = -1 + - (1/√2)

either x = -1 + (1/√2) = (1 - √2)/√2

or x = -1 - (1/√2) = -(1+√2)/√2

Answer 2

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

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

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

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

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

x square -1=3x square + 4x

x square-3x square=4x+1

-2x square= 4x+1

x square= 4x+1/2

x=4x+1/2×x

x=4x+1/2x

x= 2x+1

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