Express $\dfrac{2}{3x-1} - \dfrac{3}{1+2x}$ as a single term, in its simplest form. Answer ___

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Worked solution

1. Write the two algebraic fractions over a common denominator.

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

2. Expand and simplify the numerator.

$\frac{2(1+2x)-3(3x-1)}{(3x-1)(1+2x)}=\frac{2+4x-9x+3}{(3x-1)(1+2x)}=\frac{7-5x}{(3x-1)(1+2x)}$

Answer

$\dfrac{7-5x}{(3x-1)(1+2x)}$

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