Question

ɴᴏ sᴘᴀᴍs !

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ ɴᴇᴇᴅᴇᴅ !​

Answer 1

Multiply $\dfrac{ab}{ab}$, which is one, to the number.

$\text{L.H.S}=\dfrac{a^{-1}}{a^{-1}+b^{-1}}+\dfrac{a^{-1}}{a^{-1}-b^{-1}}$

$=\dfrac{ab}{ab} (\dfrac{a^{-1}}{a^{-1}+b^{-1}}+\dfrac{a^{-1}}{a^{-1}-b^{-1}})$

$=\dfrac{b}{b+a} +\dfrac{b}{b-a}$

After taking the LCM of the denominator,

$=\dfrac{b(b-a)}{(b+a)(b-a)} +\dfrac{b(a+b)}{(b+a)(b-a)}$

$=\dfrac{b^{2}-ab}{b^{2}-a^{2}} +\dfrac{b^{2}+ab}{b^{2}-a^{2}}$

$=\dfrac{b^{2}-ab+b^{2}+ab}{b^{2}-a^{2}}$

$=\dfrac{2b^{2}}{b^{2}-a^{2}}$

$=\boxed{-\dfrac{2b^{2}}{a^{2}-b^{2}} }$

Answer 2

Step-by-step explanation:

i hope it will help you please make as brilliant