What is the answer to (x^2+x+4)/(2x+1)= 4/x ?

The answer to (x^2+x+4)/(2x+1)= 4/x is x=-1,x=-2,x=2

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(x^2+x+4)/(2x+1)= 4/x

\frac{x ^{2} + x + 4}{2 x + 1} = \frac{4}{x}

x = - 1, x = - 2, x = 2

Solution steps

\frac{x ^{2} + x + 4}{2 x + 1} = \frac{4}{x}

Cross multiply

(x^{2} + x + 4) x = (2 x + 1) \cdot 4

Solve

(x^{2} + x + 4) x = (2 x + 1) \cdot 4 : x = - 1, x = - 2, x = 2

x = - 1, x = - 2, x = 2

Verify Solutions

Find undefined (singularity) points:

x = - \frac{1}{2}, x = 0

Combine undefined points with solutions:

x = - 1, x = - 2, x = 2

2 - \frac{2 x - 2}{2 x} = \frac{2}{2 x + 4 x}

4 - \frac{1}{x ^{2}} = 0

\frac{x}{x - 2} + \frac{2}{3} = \frac{2}{x - 2}

\frac{1}{6} + \frac{1}{9} = \frac{1}{x}

\frac{x - 9}{x ^{2} - 3 x} = \frac{12}{9 - x ^{2}}

What is the answer to (x^2+x+4)/(2x+1)= 4/x ?
The answer to (x^2+x+4)/(2x+1)= 4/x is x=-1,x=-2,x=2
Solve for x: (x^2+x+4)/(2x+1)= 4/x
The solution is x=-1,x=-2,x=2