What is the answer to ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6 ?

The answer to ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6 is x\approx-12.59937…

Solve for x: ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6

The solution is x\approx-12.59937…

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\frac{( x + 1 )}{2} + \frac{2}{x} + 1 = \frac{( x + 1 )}{3} + \frac{3}{( x + 1 )} - \frac{5}{6}

x \approx - 12.59937 \dots

Solution steps

\frac{( x + 1 )}{2} + \frac{2}{x} + 1 = \frac{( x + 1 )}{3} + \frac{3}{( x + 1 )} - \frac{5}{6}

Multiply by LCM

3 x (x + 1)^{2} + 12 (x + 1) + 6 x (x + 1) = 2 x (x + 1)^{2} + 18 x - 5 x (x + 1)

Solve

3 x (x + 1)^{2} + 12 (x + 1) + 6 x (x + 1) = 2 x (x + 1)^{2} + 18 x - 5 x (x + 1) : x \approx - 12.59937 \dots

x \approx - 12.59937 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

x \approx - 12.59937 \dots

\frac{2 ( 6 - x )}{( x - 5 )} = \frac{1}{( x - 5 ) + 6}

\frac{lo g _{10} ( 1 )}{2 ( x + 1 )} = - 1

z, w = \frac{( 4 z - 5 )}{( 2 - z )}

x, f x = \frac{ln ( 1 )}{x}

a, \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{37}{48}

What is the answer to ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6 ?
The answer to ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6 is x\approx-12.59937…
Solve for x: ((x+1))/2+2/x+1=((x+1))/3+3/((x+1))-5/6
The solution is x\approx-12.59937…