How do you solve the quadratic $4-1/x=3/x^2$ using any method?

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Answer 1 · 2016-12-27T16:52:07

Get rid of the denominators by multiplying the whole equation by $color(blue)(x^2)$

$4 color(blue)( xx x^2) - 1/x color(blue)(xx x^2) = 3/x^2 color(blue)(xx x^2)$

$4x^2 -x = 3" "larr$ make equal to 0

$4x^2 -x-3 =0$

Find factors of 4 and 3 which subtract to give 1.

$(4x+3)(x-1) =0" "larr$ either factor could be =0

If $4x+3 = 0" "rarr 4x=-3" "rarr x = -3/4$

If $x-1=0" " x = 1$

How do you solve the quadratic 4-1/x=3/x^24-1/x=3/x^2 using any method?