How do you solve $x/5 - 4/5 = 1/x$ ?

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Answer 1 · 2015-12-15T19:59:52

$x=5$ and $x=-1$

Original Equation:
$x/5-4/5=1/x$

First, subtract the two fractions on the left:
$(x-4)/5=1/x$

Next, cross multiply:
$x(x-4)=5$

Multiply the left out:
$x^2-4x=5$

Bring the $5$ over:
$x^2-4x-5=0$

Factor:
$(x-5)(x+1)=0$

Solve:
$x=5$ and $x=-1$

How do you solve x/5 - 4/5 = 1/x x/5 - 4/5 = 1/x ?