Question

solve the following pair of equations by reducing them to a pair of linear equations:5 by x-1 + 1 by x-2 = 2

Answer 1

If this question is( x - 1) + 1/(x - 2) = 2
Lcm is (x - 2)
${x}^{2} - x - 2x + 2 + 1 = 2x - 4$
${x }^{2} - 3x + 3 = 2x - 4$
${x}^{2} - 3x - 2x + 3 + 4 = 0$
${x}^{2} - 5x + 7 = 0$
Factorize it we get
$x = (5 + - \sqrt{ (- 5 {)}^{2} } - 4 \times 1 \times 7) \div 2$
$x = (5 + - \sqrt{25 - 28} ) \div 2$
$x = (5 + - \sqrt{ - 3} ) \div 2$
As discrimnent is negative it has imaginary roots.