Question

(x+1/x+2)2=x+2/x+4 step by step

Answer 1

$\large \underline{ \underline{ \text{Question:}}}$

• ${ \bigg( \frac{x + 1}{x + 2} \bigg)}^{2} = \frac{x + 2}{x + 4}$

$\large \underline{ \underline{ \text{Solution:}}}$

Given Equation,

$\implies { \bigg( \frac{x + 1}{x + 2} \bigg)}^{2} = \frac{x + 2}{x + 4}$

Can be written as,

$\implies \frac{ {(x + 1)}^{2} }{ {(x + 2)}^{2} } = \frac{x + 2}{x + 4}$

By Cross Multiplication method,

$\implies (x + 4)[ {(x + 1)}^{2}] = (x + 2)[ {(x + 2)}^{2}]$

According to Identity 1;

$[ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy ]$

Solving the problem,

$\implies (x + 4)[ {x}^{2} + 2(x)1 + {(1)}^{2} ] = (x + 2)[ {x}^{2} + 2(x)2 + {(2)}^{2} ]$

$\implies (x + 4)[ {x}^{2} + 2x + 1 ] = (x + 2)[ {x}^{2} + 4x + 4 ]$

$\implies {x}^{3} + 6{x}^{2} + 9x + 4= {x}^{3} + 6{x}^{2} + 12x + 8$

$\implies {x}^{3} + 6{x}^{2} + 9x + 4 - {x}^{3} - 6{x}^{2} - 12x - 8 = 0$

$\implies 9x + 4 - 12x - 8 = 0$

$\implies - 3x - 4 = 0$

$\implies - 3x = 4$

$\implies \boxed{ x = - \frac{4}{3}}$

Therefore,

• The value of x is - 4/3.

$\large \underline{ \underline{ \text{Required Answer:}}}$

• The value of x is - 4/3.