Question

(x+1/x+2)^2 = x+2/x+4

Answer 1

Answer:

(x+1/x+2)²=x+2/x+4

x= 1/4

Hope it helps

Answer 2

Answer:

The value of $x$ is $-\frac{4}{3}$

Step-by-step explanation:

Given expression is $(\frac{x+1}{x+2})^{2}=\frac{x+2}{x+4}$

We know $(\frac{a}{b} )^{x} =\frac{a^{x}}{b^{x}}$.

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

$(x+1)^{2}(x+4)=(x+2)(x+2)^{3}$

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

$x^{3}+4x^{2}+2x^{2}+8x+x+4=x^{3}+4x^{2}+4x+2x^{2}+8x+8$

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

Taking all the terms on one side, we get

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

$-3x-4=0$

$3x=-4$

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