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How do you solve $x + 5 = \frac{6}{x}$ $x+5=6/x$ ?

1 Answer

Jun 27, 2016

$x = 1$ $x=1$ or $x = - 6$ $x=-6$

Explanation:

Given
$XXX x + 5 = \frac{6}{x}$ $color(white)("XXX")x+5=6/x$

Multiply both sides by $x$ $x$
$XXX x^{2} + 5 x = 6$ $color(white)("XXX")x^2+5x=6$

Convert to standard form:
$XXX x^{2} + 5 x - 6 = 0$ $color(white)("XXX")x^2+5x-6=0$

Factor
$XXX (x - 1) (x + 6) = 0$ $color(white)("XXX")(x-1)(x+6)=0$ > ${: ("either",x-1=0," or ",x+6=0), (,rarr x=1,,rarr x=-6) :}$

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