Question

Plz solve by step by step explanation. ​

Answer 1

Solution:

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

$\dfrac{1(x+2)-2(x+1)}{(x+1)(x+2)} \: = \: \dfrac{3(x+4)-4(x+3)}{(x+3)(x+4)}$

$\dfrac{x+2-2x-2}{x^{2}+2x+x+2}\: = \: \dfrac{3x+12-4x-12}{x^{2}+4x+3x+12}$

$\dfrac{-x}{x^{2}+3x+2} \: = \: \dfrac{-x}{x^{2} +7x+12}$

$\dfrac{1}{x^{2}+3x+2} \: = \: \dfrac{1}{x^{2} +7x+12}$

Criss cross method

$x^{2} + 7x +12 \:=\: x^{2} +3x +2$

$7x-3x+12-2\:= \:0$

$4x \:=\:-10$

$x \:=\: \dfrac{-5}{2}$

Answer 2

❥${\purple{\underline{\underline{\large{\mathtt{ANSWER:-}}}}}}$

Value of X is -5/2.

❥${\purple{\underline{\underline{\large{\mathtt{SOLUTION:-}}}}}}$

$\frac{1}{x + 1} - \frac{2}{x + 2} = \frac{3}{x + 3} - \frac{4}{x + 4} \\ \implies \frac{x + 2 - 2(x + 1)}{(x + 1)(x + 2)} = \frac{3(x + 4) - 4(x + 3)}{(x + 3)(x + 4)} \\ \implies \frac{x + 2 - 2x - 2}{ {x}^{2} + 3x + 2 } = \frac{3x + 12 - 4x - 12}{ {x}^{2} + 7x + 12 } \\ \implies \frac{ - x}{ {x}^{2} + 3x + 2 } = \frac{ - x}{ {x}^{2} + 7x + 12 } \\ \implies\frac{1 }{ {x}^{2} + 3x + 2} = \frac{1}{ {x}^{2} + 7x + 12} \\By\: cross\: multiplication\\ \implies {x}^{2} + 7x + 12 = {x}^{2} + 3x + 2 \\ \implies 7x - 3x = 2 - 12 \\ \implies 4x = - 10 \\ \implies x = \frac{ - 5}{2}$