Question

x/x-1 + x-1/x = 2½ , solve the question by substitution method.​

Answer 1

Answer:

x/(x-1)+(x-1)/x=5/2

$x {}^{2} + (x - 1) {}^{2} \div x {} {}^{2} - x = 5 \div 2$

$x {}^{2} + x {}^{2} - 2x + 1 \div (x {}^{2} - x) = 5 \div 2$

$2x {}^{2} - 2x + 1 \div (x {}^{2} - x) = 5 \div 2$

$2(2x {}^{2} - 2x + 1) = 5(x {}^{2} - x)$

$4x {}^{2} - 4x + 2 = 5x {}^{2} - 5x$

$4x {}^{2} - 4x + 2 - 5x {}^{2} + 5x = 0$

$- x {}^{2} + x + 2 = 0$

$- (x {}^{2} - x - 2) = 0$

$x {}^{2} - x - 2 = 0$

$x {}^{2} - 2x + x - 2 = 0$

$x(x + 1) - 2(x + 1) = 0$

$(x + 1)(x - 2) = 0$

$x + 1 = 0$

$x = - 1$

$x - 2 = 0$

$x = 2$