X+2/x-3 + x-3/x+2 = 5/2

Question 1

Question 2

Answer:

x_(1) =(-17- √(129))/(2), x_(2) =(-17+ √(129))/(2)

Explanation:

(x + 2)/(x + 3) + (x - 3)/(x + 2) = (5)/(2)

(x + 2)/(x + 3) + (x - 3)/(x + 2) - (5)/(2) = 0

$\frac{2(x + 2 {)}^(2) + 2(x + 3) * (x - 3) - 5(x + 3) * (x + 2) }{2(x + 3) * (x + 2)} = 0$

$\frac{2(x + 2 {)}^(2) + 2( {x}^(2) - 9) + ( - 15x - 15) * (x + 2) }{2(x + 3) * (x + 2)} = 0$

$\frac{2( {x}^(2) + 4x + 4) - 3 {x}^(2) - 48 - 25x}{2(x + 3) * (x + 2)} = 0$

$\frac{2 {x}^(2) + 8x + 8 - 3 {x}^(2) - 48 - 25x }{2(x + 3) * (x + 2)} = 0$

$\frac{ - {x}^(2) - 17x - 40 }{2(x + 3) * (x + 2)} = 0$

${x}^(2) + 17x + 40 = 0$

$x = \frac{ - 17± \sqrt{ {17}^(2) - 4 * 1 * 40 } }{2 * 1}$

x = ( - 17± √(289 - 160) )/(2)

x = ( - 17± √(129) )/(2)

x_(1) =(-17- √(129))/(2), x_(2) =(-17+ √(129))/(2)

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