Question 344883
Solving for x. Since x cannot be zero, we can go ahead and multiply both sides of the equation by x. This will eliminate the fraction:
{{{xy = x^2 + 1}}}
Next we'll get one side equal to zero (because we are about to use the Quadratic Formula) by subtracting xy from each side:
{{{0 = x^2 -xy + 1}}}
Because multiplication is commutative and because it may make the next step clearer, I'm going to rewrite xy as yx:
{{{0 = x^2 -yx + 1}}}
Now we will use the Quadratic formula with a = 1, c = 1 and b = -y! This is an unusual yet still valid way to use the Quadratic Formula.
{{{x = (-(-y) +- sqrt((-y)^2 - 4(1)(1)))/2(1)}}}
which simplifies as follows:
{{{x = (-(-y) +- sqrt(y^2 - 4(1)(1)))/2(1)}}}
{{{x = (y +- sqrt(y^2 - 4))/2}}}
This equation has x solved for in terms of y.