Write as a single fraction in its simplest form $\frac{3}{2a-1} - \frac{2}{1-2a}$ . Answer ___

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Worked solution

1. Rewrite the second denominator so both fractions have the same denominator.

Since $1-2a=-(2a-1)$ ,
$\frac{2}{1-2a}=\frac{2}{-(2a-1)}=-\frac{2}{2a-1}.$

2. Combine the fractions and simplify the numerator.

$\frac{3}{2a-1}-\frac{2}{1-2a}=\frac{3}{2a-1}-\left(-\frac{2}{2a-1}\right)$
$=\frac{3}{2a-1}+\frac{2}{2a-1}=\frac{5}{2a-1}.$

Answer

$\dfrac{5}{2a-1}$

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