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

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Worked solution

1. Write both fractions with a common denominator.

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

2. Expand and simplify the numerator.

$\frac{2(2x+1)-3(x-2)}{(x-2)(2x+1)}=\frac{4x+2-3x+6}{(x-2)(2x+1)}=\frac{x+8}{(x-2)(2x+1)}$

Answer

$\dfrac{7-4x}{(x-2)(2x+1)}$

AI analysis — may contain mistakes.

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