How do you solve $x-7+14/x=2$ and check for extraneous solutions?

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Answer 1 · 2016-12-22T14:57:06

${7, 2}$ with $x != 0$

Put on a common denominator $(x)$ .

$(x^2 - 7x + 14)/x = 2$

$x^2 - 7x + 14 = 2x$

$x^2 - 9x + 14 = 0$

$(x - 7)(x - 2) = 0$

$x = 7 and 2$

CHECK

$7 - 7 + 14/7 =^? 2$

$0 + 2 = 2" "color(green)(√)$

$2 - 7 + 14/2 =^? 2$

$-5 + 7 = 2" "color(green)(√)$

Hopefully this helps!

How do you solve x-7+14/x=2x-7+14/x=2 and check for extraneous solutions?