Question

(2+x) /(4+x) = (4+x) /(5+x)​

Answer 1

$x^{2}$Answer:

Step-by-step explanation:

On cross multiplication

(2+x)(5+x) =(4+x)(4+x)

⇒10+2x+5x+ =16+4x+4x+$x^{2}$

⇒10-16+7x-8x+$x^{2}$-$x^{2}$ = 0

⇒  -6 - x=0

⇒x= - 6

Answer 2

$\huge\red{ANSWER}\pink{:}$

$\frac{2 + x}{4 + x} = \frac{x + 4}{x + 5} \\ \frac{x + 2}{x + {2}^{2} } = \frac{x + 4}{x + 5} \\ (x + 5) \: (x + 2) \: = (x + 4) \: (x + 4) \: \\ (x + 5) \: (x + 2) = ( {x + 4)}^{1 + 1} \\ (x + 5) \: (x + 2) = {(x + 4)}^{2} \\ xx + x.2 + 5x + 5.2 = {x}^{2} + 2x.4x {4}^{2} \\ {x}^{1 + 1} + 2x + 5x + 10 = {x}^{2} + 2.4x + 16 \\ {x}^{2} + 2x + 5x + 10 = {x}^{2} + 8x + 16 \\ {x}^{2} + 7x + 10 = {x}^{2} + 8x + 16 \\ 7x + 10 = 8x + 16 \\ (7x + 10) + ( - 8x - 10) = (8x + 16 )+( - 10 - 8x) \\ (7x + 10)( - 8x - 10) = (8x + 16) + ( - 8x - 10) \\ 7x - + 10 - 8x - 10 = 8x + 16 - 8x - 10 \\ 7x - 8x + 10 - 10 = 8x - 8x + 16 - 10 \\ = - x = 6 \\ = x = - 6$