Question

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

Answer 1

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`