Question

2/x+2 - 1/x+1 = 4/x+4 - 3/x+3​

Answer 1

Question:

$\frac{2}{x + 2} - \frac{1}{x + 1} = \frac{4}{x + 4} - \frac{3}{x + 3}$

Solution:

Cross multiplying

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

Hope it helps you.