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

The answer to (x+2)/(3x-1)+1=(6-x)/(x+1) is x=1

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(x+2)/(3x-1)+1=(6-x)/(x+1)

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

x = 1

Solution steps

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

Multiply by LCM

(x + 2) (x + 1) + (x + 1) (3 x - 1) = (6 - x) (3 x - 1)

Solve

(x + 2) (x + 1) + (x + 1) (3 x - 1) = (6 - x) (3 x - 1) : x = 1

x = 1

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{3}, x = - 1

Combine undefined points with solutions:

x = 1

2 x - \frac{7}{x - 6} = x

g, c = \frac{d}{g}

\frac{3 - 5 x}{x - 1} = x^{2} + 2 x - 3

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

\frac{x ^{2}}{x - 10} = \frac{100}{x - 10} - 10

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