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Question
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solution
`("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
(x + 3)(2x - 3) = (3x - 7)(x + 2)
2x2 + 6x - 3x - 9 = 3x2 - 7x + 6x - 14
2x2 + 3x - 9 = 3x2 - x - 14
(3 - 2)x2 +(-1 - 3) x + (- 14 + 9) = 0
x2 - 4x -5= 0
x2 + x - 5x - 5 = 0
x (x+ 1) - 5 (x + 1) = 0
( x + 1)(x - 5) = 0
(x+ 1)= 0, (x - 5)= 0
X = -1 , x = 5
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