Question

x + 2 / x - 1 = x- 1 / x + 3 + 7​ , find the roots

Answer 1

Answer:

$\frac{x + 2}{x - 1} = \frac{x - 1}{x + 3 + 7}$

(X + 2 )(X + 3 + 7 ) = (X - 1 )(X - 1 )

X(X + 3 + 7 ) + 2 (X + 3 + 7 ) = X ( X - 1 ) -1 ( X - 1 )

X

${x}^{2} + 3x + 7x + 2x + 6 + 14 = {x}^{2} - x - x + 1$

${x}^{2} + 12x + 20 = {x}^{2} - 2x + 1$

${x}^{2} + 2x + 10x + 20 = {x}^{2} - x - x + 1$

x ( x + 2 ) + 10 ( x + 2 ) = x ( x - 1 ) - 1( x - 1 )))

( x + 2 ) ( x+ 10 ) = ( x- 1 ) ( x- 1 )

( x = - 2 or x = -10 ) = x = 1