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Question
Solve the following equation using the formula:
`(2x)/(x - 4) + (2x - 5)/(x - 3) = 8 1/3`
Solution
`(2x)/(x - 4) + (2x - 5)/(x - 3) = 8 1/3`
`=> (2x(x - 3) + (x - 4)(2x - 5))/((x - 4)(x - 3)) = 25/3`
`=>(2x^2 - 6x + 2x^2 - 5x - 8x + 20)/(x^2 - 3x - 4x + 12) = 25/3`
`=> (4x^2 - 19x + 20)/(x^2 - 7x + 12) = 25/3`
`=>` 25x2 – 175x + 300 = 12x2 – 57x + 60
`=>` 13x2 – 118x + 240 = 0
Here a = 13, b = −118 and c = 240
Then `x = (-b + -sqrt(b^2 - 4ac))/(2a)`
= `(-(-118) +- sqrt((-118)^2 - 4(sqrt(13))(240)))/(2(13))`
= `(118 +- sqrt1444)/26`
= `(118 +- 38)/26`
`x = (118+38)/26` or `x = (118-38)/26`
`therefore x = (118 + 38)/26`
`=>` x = 6
`x = (118-38)/26`
`therefore x = (40/13)`
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