Question 41306
Find the positive root:
{{{2x^-1 + (x-1)^-1 = 4}}} Simplify.
{{{2/x + 1/(x-1) = 4}}} Add the fractions on the left side.
{{{(2(x-1) + x)/(x(x-1)) = 4}}} Simplify.
{{{(3x-2)/(x^2-x) = 4}}} Multiply both sides by x^2-x
{{{3x-2 = 4(x^2-x)}}} Simplify.
{{{3x-2 = 4x^2-4x}}} Subtract 3x-2 from both sides.
{{{4x^2-7x+2 = 0}}}} Solve the quadratic equation by the quadratic formula:{{{x=(-b+-sqrt(b^2-4ac))/2a}}}

{{{x = (-(-7)+-sqrt((-7)^2-4(4)(2)))/2(4)}}} Simplify.
{{{x = (7+-sqrt(49-32))/8}}}
{{{x = (7+-sqrt(17))/8}}}

One positive root is:
{{{x = (7/8)+(sqrt(17))/8}}} = 1.40 (approximately)

The other positive root is:
{{{x = (7/8)-(sqrt(17))/8}}} = 0.36 (approximately)