Question

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

Answer 1

Answer:

$\frac{1}{(x + 1)} - \frac{2}{(x + 2)} = \frac{3}{(x + 3)} - \frac{4}{(x + 4)} \\ \frac{1( x+ 2) - 2(x + 1)}{x(x + 2) + 1(x + 2)} = \frac{3(x + 4) - 4(x + 3)}{x(x + 4) + 3(x + 4)} \\ \frac{x + 2 - 2x - 2}{ {x}^{2} + 2x + x + 2} = \frac{3x + 12 - 4x - 12}{ {x}^{2} + 4x + 3x + 12 } \\ \frac{ - x}{ {x}^{2} + 3x + 2} = \frac{ - x}{ {x}^{2} + 7x + 12 } \\ - x({x}^{2} + 7x + 12) = - x({x}^{2} + 3x + 2) \\ - {x}^{3} - 7{x}^{2} - 12x = - {x}^{3} - 3{x}^{2} - 2x \\ - 7{x}^{2} + 3{x}^{2} - 12x + 2x = 0 \\ - 4{x}^{2} - 10x = 0 \\ - 2x(2{x} + 5) = 0 \\ 2x + 5 = 0 \\ x = \frac{ - 5}{2}$