Question

Solve the following equation using the formula: 

`(2x)/(x - 4) + (2x - 5)/(x - 3) = 8 1/3` 

Answer 1

`(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)`