Question

solve the equation by factories
x/x+1 + x+1/x =5/2​

Answer 1

Answer:

At first,we have,

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{5}{2}$

$or \: \frac{ {x}^{2} + {(x + 1)}^{2} }{x(x + 1)} = \frac{5}{2}$(by cross multiplying)

$or \: \frac{ {x}^{2} + {x}^{2} + 2x + 1 }{ {x}^{2} + x} = \frac{5}{2}$

$or \: \frac{2( {2x}^{2} + 2x + 1) }{ {x}^{2} + x} = 5$

Now,

$or \: \: 4 {x}^{2} + 4x + 2 = 5( {x}^{2} + x)$

$or \: \: 4 {x}^{2} + 4x + 2 = 5 {x}^{2} + 5x$

By transposing the terms from RHS to

LHS,we get,

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

Now, after simplification, we get

$or \: \: - {x}^{2} - x + 2 = 0$

Taking minus sign common,we get,

$or \: - ( {x}^{2} + x - 2) = 0$

$or \: {x}^{2} + x - 2 = 0$

By middle term factorisation ,we get,

$or \: \: {x}^{2} + 2x - x - 2 = 0$

$or \: x(x + 2) - 1(x + 2) = 0$

$or \: \: (x + 2)(x - 1) = 0$

$or \: x = - 2 \: or \: x = 1$