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

The answer to x/((x+1))+2=((2x-3))/x+3/((x(x+1))) is x=-3

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

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

x = - 3

Solution steps

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

Multiply by LCM

x^{2} + 2 x (x + 1) = (2 x - 3) (x + 1) + 3

Solve

x^{2} + 2 x (x + 1) = (2 x - 3) (x + 1) + 3 : x = 0, x = - 3

x = 0, x = - 3

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Since the equation is undefined for:

0

x = - 3

\frac{( x - b )}{( x - a )} + \frac{( x - a )}{( b - a )} = 1

\frac{4 x + 1}{3 x} = 8

\frac{8 x ^{3}}{2 \cdot x ^{- 5}} = 4 x^{8}

\frac{( 25 )}{1.5} = \frac{50}{a}

x + \frac{1}{x} = 3, x + \frac{1}{( x )}

What is the answer to x/((x+1))+2=((2x-3))/x+3/((x(x+1))) ?
The answer to x/((x+1))+2=((2x-3))/x+3/((x(x+1))) is x=-3
Solve for x: x/((x+1))+2=((2x-3))/x+3/((x(x+1)))
The solution is x=-3