What is the answer to (3a)/(2a+1)-4/(2a-1)=1 ?

The answer to (3a)/(2a+1)-4/(2a-1)=1 is a=(11+sqrt(145))/4 ,a=(11-sqrt(145))/4

Solve for a: (3a)/(2a+1)-4/(2a-1)=1

The solution is a=(11+sqrt(145))/4 ,a=(11-sqrt(145))/4

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\frac{3 a}{2 a + 1} - \frac{4}{2 a - 1} = 1

a = \frac{11 + 145}{4}, a = \frac{11 - 145}{4}

Decimal

a = 5.76039 \dots, a = - 0.26039 \dots

Solution steps

\frac{3 a}{2 a + 1} - \frac{4}{2 a - 1} = 1

Multiply by LCM

3 a (2 a - 1) - 4 (2 a + 1) = (2 a + 1) (2 a - 1)

Solve

3 a (2 a - 1) - 4 (2 a + 1) = (2 a + 1) (2 a - 1) : a = \frac{11 + 145}{4}, a = \frac{11 - 145}{4}

a = \frac{11 + 145}{4}, a = \frac{11 - 145}{4}

Verify Solutions

Find undefined (singularity) points:

a = - \frac{1}{2}, a = \frac{1}{2}

Combine undefined points with solutions:

a = \frac{11 + 145}{4}, a = \frac{11 - 145}{4}

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

\frac{13}{x} = 10 - x

- \frac{1}{x - 1} + 7 = - \frac{1}{x ^{2} - x}

\frac{10 x ^{2} - 5 x + 8}{5 x ^{2} + 9 x - 19} = 2

x, z = \frac{y}{x}

What is the answer to (3a)/(2a+1)-4/(2a-1)=1 ?
The answer to (3a)/(2a+1)-4/(2a-1)=1 is a=(11+sqrt(145))/4 ,a=(11-sqrt(145))/4
Solve for a: (3a)/(2a+1)-4/(2a-1)=1
The solution is a=(11+sqrt(145))/4 ,a=(11-sqrt(145))/4