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Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^...

Prove that: `(a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(b^2-a^2)`

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To prove the equation \[ \frac{a^{-1}}{a^{-1} + b^{-1}} + \frac{a^{-1}}{a^{-1} - b^{-1}} = \frac{2b^2}{b^2 - a^2} \] we will simplify the left-hand side (LHS) step by step. ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+...

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  2. If a b c=1, show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

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  3. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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  4. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

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  5. Find the value of x , if 5^(x-3)\xx\ 3^(2x-8)=225

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  6. Solve the following equations: 2^(x-5)=256 (ii) 2^(x+3)=4^(x-1)

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  7. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

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  8. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

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  9. Solve the equation for x 5^(2x+1)=6. 5^x-1

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  10. 3(a^4b^3)^10xx5(a^2b^2)^3

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  11. Simplify that: (2x^(-2)y^3)^3

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  12. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  13. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  14. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  15. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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  16. If a=3 and b=-2, find the values of: (i)\ a^a+b^b (ii)\ a^b+b^a (iii...

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  17. Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c...

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  18. Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

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  19. Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

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  20. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

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