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Question
Solve the following equation using the formula:
`(2x + 3)/(x + 3) = (x + 4)/(x + 2)`
Solution
`(2x + 3)/(x + 3) = (x + 4)/(x + 2)`
`\implies` (2x + 3)(x + 2) = (x + 3)(x + 4)
`\implies` 2x2 + 4x + 3x + 6 = x2 + 4x + 3x + 12
`\implies` x2 – 6 = 0
Here a = 1, b = 0 and c = – 6
Then `x =(-b +- sqrt(b^2 - 4ac))/(2a)`
= `(-(0) +- sqrt((0)^2 - 4(1)(-6)))/(2(1))`
= `(0 +- sqrt(24))/2`
= `(0 +- 2sqrt(6))/2`
= `-sqrt(6)` and `sqrt(6)`
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