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

The answer to (2q)/(2q+3)-(2q)/(2q-3)=1 is q=(3(sqrt(2)-1))/2 ,q=-(3(1+sqrt(2)))/2

Solve for q: (2q)/(2q+3)-(2q)/(2q-3)=1

The solution is q=(3(sqrt(2)-1))/2 ,q=-(3(1+sqrt(2)))/2

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\frac{2 q}{2 q + 3} - \frac{2 q}{2 q - 3} = 1

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

Decimal Notation

q = 0.62132 \dots, q = - 3.62132 \dots

Solution steps

\frac{2 q}{2 q + 3} - \frac{2 q}{2 q - 3} = 1

Multiply by LCM

2 q (2 q - 3) - 2 q (2 q + 3) = (2 q + 3) (2 q - 3)

Solve

2 q (2 q - 3) - 2 q (2 q + 3) = (2 q + 3) (2 q - 3) : q = \frac{3 ( 2 - 1 )}{2}, q = - \frac{3 ( 1 + 2 )}{2}

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

Verify Solutions

Find undefined (singularity) points:

q = - \frac{3}{2}, q = \frac{3}{2}

Combine undefined points with solutions:

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

\frac{3}{7 x - 1} + \frac{1}{x} = 0

\frac{x ^{2} - 64}{8 x - x ^{2}} = 0

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

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

\frac{2 x}{2 x + 3} + \frac{6}{4 x + 6} = 5

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