Solve 2a-1/2a-2a/2a-1-1/2a-4a | Microsoft Math Solver

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

Combine 2a and -4a to get -2a.

\frac{\left(2a-1\right)\left(2a-1\right)}{2a\left(2a-1\right)}-\frac{2a\times 2a}{2a\left(2a-1\right)}-\frac{1}{-2a}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 2a-1 is 2a\left(2a-1\right). Multiply \frac{2a-1}{2a} times \frac{2a-1}{2a-1}. Multiply \frac{2a}{2a-1} times \frac{2a}{2a}.

\frac{\left(2a-1\right)\left(2a-1\right)-2a\times 2a}{2a\left(2a-1\right)}-\frac{1}{-2a}

Since \frac{\left(2a-1\right)\left(2a-1\right)}{2a\left(2a-1\right)} and \frac{2a\times 2a}{2a\left(2a-1\right)} have the same denominator, subtract them by subtracting their numerators.

\frac{4a^{2}-2a-2a+1-4a^{2}}{2a\left(2a-1\right)}-\frac{1}{-2a}

Do the multiplications in \left(2a-1\right)\left(2a-1\right)-2a\times 2a.

\frac{-4a+1}{2a\left(2a-1\right)}-\frac{1}{-2a}

Combine like terms in 4a^{2}-2a-2a+1-4a^{2}.

\frac{-4a+1}{2a\left(2a-1\right)}-\frac{-\left(2a-1\right)}{2a\left(2a-1\right)}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a\left(2a-1\right) and -2a is 2a\left(2a-1\right). Multiply \frac{1}{-2a} times \frac{-\left(2a-1\right)}{-\left(2a-1\right)}.

\frac{-4a+1-\left(-\left(2a-1\right)\right)}{2a\left(2a-1\right)}

Since \frac{-4a+1}{2a\left(2a-1\right)} and \frac{-\left(2a-1\right)}{2a\left(2a-1\right)} have the same denominator, subtract them by subtracting their numerators.

\frac{-4a+1+2a-1}{2a\left(2a-1\right)}

Do the multiplications in -4a+1-\left(-\left(2a-1\right)\right).

\frac{-2a}{2a\left(2a-1\right)}

Combine like terms in -4a+1+2a-1.

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

Cancel out 2a in both numerator and denominator.