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Question
Solve the following equation using the formula:
`(x - 1)/(x - 2) + (x - 3)/(x - 4) = 3 1/3`
Solution
`(x - 1)/(x - 2) + (x - 3)/(x - 4) = 3 1/3`
`=> ((x - 1)(x - 4) + (x - 2)(x - 3))/((x - 2)(x - 4)) = 10/3`
`=> (x^2 - 4x - x + 4 + x^2 - 3x - 2x + 6)/(x^2 - 4x - 2x + 8) = 10/3`
`=> (2x^2 - 10x + 10)/(x^2 - 6x + 8) = 10/3`
`=>` 10x2 – 60x + 80 = 6x2 – 30x + 30
`=>` 4x2 – 30x + 50 = 0
`=>` 2x2 – 15x + 25 = 0
Here a = 2, b = −15 and c = 25
Then `x = (-b +- sqrt(b^2-4ac))/(2a)`
= `(-(-15) +- sqrt((-15)^2 - 4(2)(25)))/(2(2))`
= `(15 +- sqrt(25))/4`
= `(15 +- 5)/4`
= `(15 + 5)/4` and `(15 - 5)/4`
= 5 and `5/2`
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