Question
Expand $: \left(2 x-\frac{1}{x}\right)\left(3 x+\frac{2}{x}\right)$
✓
Answer
$ \left(2 x-\frac{1}{x}\right)\left(3 x+\frac{2}{x}\right)$
$ =2 x\left(3 x+\frac{2}{x}\right)-\frac{1}{x}\left(3 x+\frac{2}{x}\right)$
$ =6 x^2+2 x \times \frac{2}{x}-\frac{1}{x} \times 3 x-\frac{1}{x} \times \frac{2}{x}$
$ =6 x^2+4-3-\frac{2}{x^2}$
$ =6 x^2+1-\frac{2}{x^2}$
$ =2 x\left(3 x+\frac{2}{x}\right)-\frac{1}{x}\left(3 x+\frac{2}{x}\right)$
$ =6 x^2+2 x \times \frac{2}{x}-\frac{1}{x} \times 3 x-\frac{1}{x} \times \frac{2}{x}$
$ =6 x^2+4-3-\frac{2}{x^2}$
$ =6 x^2+1-\frac{2}{x^2}$
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