Question

x³+12x-20/3x-5 = x²+8x+12/2x+3 Solve the equation.

Answer 1

Step-by-step explanation:

To solve the equation,first cross multiply

$\frac{ {x}^{3} + 12x - 20 }{3x - 5} = \frac{ {x}^{2} + 8x + 12 }{2x + 3} \\ \\ (2x + 3)({x}^{3} + 12x - 20) = (3x - 5)({x}^{2} + 8x + 12) \\ \\ 2 {x}^{4} + 24 {x}^{2} - 40x + 3 {x}^{3} + 36x - 60 = 3 {x}^{3} + 24 {x}^{2} + 36x - 5 {x}^{2} - 40x - 60 \\ \\ 2 {x}^{4} + 24 {x}^{2} + 3 {x}^{3} - 4x - 60 = 3 {x}^{3} + 24 {x}^{2} - 5 {x}^{2} - 4x - 60 \\ \\ 2 {x}^{4} + 24 {x}^{2} + 3 {x}^{3} - 4x - 60 - 3 {x}^{3} - 24 {x}^{2} + 5 {x}^{2} + 4x + 60 = 0 \\ \\ 2 {x}^{4} + 5 {x}^{2} = 0 \\ \\ {x}^{2} (2 {x}^{2} + 5) = 0 \\ \\ {x}^{2} = 0 \\ \\ x = 0 \\ \\ 2 {x}^{2} + 5 = 0 \\ \\ 2 {x}^{2} = - 5 \\ \\ {x}^{2} = \frac{-5}{2}$

Hope it helps you