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

The answer to 2((2x-1)/(x+3))-3((x+3)/(2x-1))=5 is x=-10,x=-1/5

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2((2x-1)/(x+3))-3((x+3)/(2x-1))=5

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

x = - 10, x = - \frac{1}{5}

Decimal Notation

x = - 10, x = - 0.2

Solution steps

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

Multiply by LCM

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

Solve

2 (2 x - 1)^{2} - 3 (x + 3)^{2} = 5 (x + 3) (2 x - 1) : x = - 10, x = - \frac{1}{5}

x = - 10, x = - \frac{1}{5}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = \frac{1}{2}

Combine undefined points with solutions:

x = - 10, x = - \frac{1}{5}

x, \frac{1}{x} + \frac{1}{y} = 1

2 (\frac{x ^{2} + 1}{( x ^{2} )}) - 3 (\frac{x - 1}{x}) - 4 = 0

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

\frac{31}{2 x} = 56

\frac{2}{( 3 x )} + \frac{( 2 x - 1 )}{( 4 x ^{2} )} = \frac{5}{( 12 x )}

What is the answer to 2((2x-1)/(x+3))-3((x+3)/(2x-1))=5 ?
The answer to 2((2x-1)/(x+3))-3((x+3)/(2x-1))=5 is x=-10,x=-1/5
Solve for x: 2((2x-1)/(x+3))-3((x+3)/(2x-1))=5
The solution is x=-10,x=-1/5