Question

Solve the following quadratic equations by factorization: 

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

Answer 1

`4/(x+2)-1/(x+3)=4/(2x+1)` 

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

⟹` (4x+12-x-2)/(x^2+2x+3x+6)=4/(2x+1)` 

⟹`( 3x+10)/(x^2+5x+6)=4/(2x+1)` 

⟹ `(3x+10) (2x+1) = 4(x^2+5x+6)` 

⟹ `6x^2+3x+20x+10=4x^2+20x+24` 

⟹ `2x^2 +3x – 14 = 0`
⟹` 2x^2 + 7x – 4x – 14 = 0`
⟹` x (2x + 7) – 2(2x + 7) = 0`
⟹` (2x + 7) ( x – 2) = 0`
If `2x + 7 = 0 Or x – 2 = 0` 

`Then x= -7/2 or x=2`