Question

solve please simplify it ​

Answer 1

Answer:

I hope you understand..........

Answer 2

Question ; simplify it :

$\displaystyle\longmapsto\sf \dfrac{1}{1 + a^{n - m} } + \dfrac{1}{1 + a^{m - n}}$

Solution :

$\star$ Law of exponent to be used :

$\longmapsto\displaystyle\underline{\boxed{\sf x^{a - b} = \dfrac{x^a}{x^b} }}}$

Now calculation :

$\longmapsto\sf \dfrac{1}{1 + a^{n - m}} + \dfrac{1}{1 + a^{m - n}} \\\\ \\ \longmapsto\sf \dfrac{1}{1 + \dfrac{a^n}{a^m}} + \dfrac{1}{1 + \dfrac{a^m}{a^n}} \\\\ \\ \longmapsto\sf \dfrac{1}{ \dfrac{a^m + a^n}{a^m} } + \dfrac{1}{ \dfrac{a^n + a^m}{a^n}} \\\\ \\ \longmapsto\sf \dfrac{a^m}{a^m + a^n} + \dfrac{a^n}{a^m + a^n} \\\\ \\ \longmapsto\sf \dfrac{a^m + a^n}{a^m + a^n} \\\\ \\ \longmapsto\Large\underline{\boxed{\sf{1}}}$

$\therefore\underline{\textsf{Required value for expression}} = \underline{\boxed{\bold{ 1 }}}$

$\rule{250}{1}$

$\boxed{\begin{minipage} {6 cm} \\ \star \ \underline{\bold{Law \ of \ exponents}} : \\ \\ \star \ \sf x^a * x^b = x^{a + b} \\ \\ \star \ \sf\dfrac{x^a}{x^b} = x^{a - b} \\ \\ \star \ \sf (xy)^a = x^a * x^b \\ \\ \star\ \sf (x^a)^b = x^{ab} \\ \\ \star\ \sf x^{-a} = \dfrac{1}{x^a} \\\\ \star \ \sf\bigg(\dfrac{x}{y}\bigg)^a = \dfrac{x^a}{y^a} \\\\ \star \ \sf x^0 = 1 \ (x \neq 0) \end{minipage}}$