Question

Solve the following quadratic equations by factorization: 

`(3x-2)/(2x-3)=(3x-8)/(x+4)` 

 

Answer 1

`(3x-2)/(2x-3)=(3x-8)/(x+4)`   

⟹ (3x – 2) (x + 4) = (2x – 3) (3x – 8)
⟹ `3x^2 + 12x – 2x – 8 = 6x^2 – 16x – 9x + 24`
⟹ `3x^2 + 10x – 8 = 6x^2 – 25x + 24`
⟹` 3x^2 – 35x + 32 = 0`
⟹ `3x^2 – 32x – 3x + 32 = 0`
⟹ x(3x – 32) – 1(3x – 32) = 0
⟹ (x – 1) (3x – 32) = 0 

If x – 1 = 0  Or  3x – 32 = 0 

`⟹ x = 1    Or   x=32/3=10 2/3`