Question

Solve the following equation using the formula: 

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

Answer 1

`(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`