Question

Solve the following equation using the formula: 

`(2x + 3)/(x + 3) = (x + 4)/(x + 2)` 

Answer 1

`(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)`