Solve this problem?

Question

How would I solve 4 + 5 / x^2 = 2/x ????

Answer 1

First multiply by x^2 to move all the x's out of the denominators...

4 + 5/x^2 = 2/x
4x^2 + 5 = 2x
4x^2 - 2x + 5 = 0

x = ( -(-2) +/- sqrt(2^2 - 4*4*2 ))/ (2*4)
x = (2 +/- sqrt(-28))/8
x = (1 +/- sqrt(7)i)/4

The discriminant (b^2 - 4ac = -28) is negative so there are no solutions except in imaginary numbers.

Answer 2

Multiply all terms by x² to get:

4x² + 5 = 2x

4x² - 2x + 5 = 0 it does not have real solutions though.

Check the equation was copied correctly.