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This is a fixed, unmarked, question:

\n

Show that (x1)/((1/x3)-(1/x2))) = (x1x2x3)/(x2-x3)

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Is $\\displaystyle{\\frac{x_1}{\\frac{1}{x_3}-\\frac{1}{x_2}}}$ is equal to $\\displaystyle{\\frac{x_1 x_2 x_3}{x_2-x_3}}$?

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Write your full working down on paper, then check it against the advice.

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\\[\\begin{align*}\\frac{x_1}{\\frac{1}{x_3}-\\frac{1}{x_2}} &= \\frac{x_1}{\\frac{x_2}{x_2x_3}-\\frac{x_3}{x_2 x_3}}\\\\&= \\frac{x_1}{\\frac{x_2-x_3}{x_3x_2}}\\\\&=\\frac{x_1}{1}\\times\\frac{x_2x_3}{x_2-x_3}\\\\&=\\frac{x_1x_2x_3}{x_2-x_3},\\quad\\textrm{as required.} \\end{align*}\\]

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