How do you solve $\frac{1}{x} + \frac{2}{3} = 2$ $1/x+2/3=2$ and check for extraneous solutions?

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How do you solve $\frac{1}{x} + \frac{2}{3} = 2$ $1/x+2/3=2$ and check for extraneous solutions?

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Answer 1 · 2017-01-15T22:55:25

$x = \frac{3}{4}$ $x=3/4$

Explanation:

Multiply through by $3 x$ $3x$ to get $3 + 2 x = 6 x$ $3+2x=6x$ which is linear with the only solution $x = \frac{3}{4}$ $x=3/4$ . Check this back in the original equation: $\frac{4}{3} + \frac{2}{3} = 2$ $4/3+2/3=2$

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How do you solve $\frac{1}{x} + \frac{2}{3} = 2$ $1/x+2/3=2$ and check for extraneous solutions?

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How do you solve $\frac{1}{x} + \frac{2}{3} = 2$ $1/x+2/3=2$ and check for extraneous solutions?