Solve the following equations for x in terms of a b and c a1

Solve the following equations for x in terms of a, b and c. a(1 + squarerootx/x minus 1) = b x =

Solution

a( 1 + x)/(x - 1) = b or, a( 1 + x) = b ( x -1) ( if x 1, as division by 0 is not defined) or, a + a x = bx - b or, ax = bx - ( a + b) so that ( a x)² = [bx -(a + b)]² or, a²x = b²x² - 2b( a +b)+ (a+b )² or, a²x = b²x² - 2ab - 2b² + a²+ 2ab + b² or, a²x = b²x² + a² -b²or, b²x²- a²x + (a² - b²) = 0.Therefore, on using the quadratic formula, x = [ -( -a²) ± { ( -a²)² - 4b²(a²- b²)} ]/2b² or, x = [ a² ± { a⁴ -4a²b² + 4b⁴}/2b² or,x = [ a² ± ( a²-2b²)² ] / 2b² or, x = [ a² ± ( a²-2b²)]/ 2b². Thus, either x = 2(a² - b² )/ 2b² =   (a² - b² )/ b² or, x = 2b²/2b² = 1. However x can not be equal to 1 as division by 0 is not defined. Therefore, x = (a² - b² )/ b²