Question

don't try to give silly answers or you will be reported

I want answer with explanation!​

Answer 1

Answer:

option (2) is correct

$\frac{2 + x}{2 - x}$

Step-by-step explanation:

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

Answer 2

Question :-

Which of the following is the simplied form of

$\sf\dfrac{1 + x + \dfrac{x^2}{4}}{1 - \dfrac{x^2}{4}}$

Answer :-

$\implies\sf\dfrac{1 + x + \dfrac{x^2}{4}}{1 - \dfrac{x^2}{4}}$

$\implies\sf\dfrac{\dfrac{4 + 4x + x^2}{4}}{ \dfrac{ 4 - x^2}{4}}$

$\implies\sf\dfrac{\dfrac{2^2 + 2 \times 2 \times x + x^2}{4}}{ \dfrac{ 2^2 - x^2}{4}}$

• a² + 2ab + b² = ( a + b )²
• a² - b² = ( a + b ) ( a - b )

$\implies\sf\dfrac{\dfrac{(2 + x)^2}{4}}{ \dfrac{ (2+x)(2-x)}{4}}$

$\implies\sf\dfrac{( 2 + x)^2 \times \not4}{(2 + x)(2 - x) \times \not4}$

$\implies\sf\dfrac{(2 + x)(2 + x)}{(2+ x)(2 - x)}$

$\implies\sf\dfrac{ 2 + x}{2 - x}$

$\boxed{\sf\dfrac{1 + x + \dfrac{x^2}{4}}{1 - \dfrac{x^2}{4}} = \dfrac{ 2 + x}{2 - x}}$