2x 1x3x+2x= (2x)(3x) (1/x)(3x) + (2/x)(2x) (1/x)(2/x) = 6x^2 (3 4) 2/x^2 = 6x^2 ( 1) 2/x^2 = 6x^2 +1 2/x^2 ...

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Introduction to Algebraic Identities

Expand 2x-1x3...

Question

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

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Solution

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

= $6 x^{2} - (3 - 4) - \frac{2}{x^{2}}$

= $6 x^{2} - (- 1) - \frac{2}{x^{2}}$

= $6 x^{2} + 1 - \frac{2}{x^{2}}$

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