Prove that the value of the expression does not depend on a, b, c and x
[math]\frac{4}{a^{-x}+\frac{1}{b^{-x}+\frac{1}{c^{-x}}}} \div \frac{1}{a^{-x}+ \frac{1}{b^{-x}}}- \frac{4}{b^{-x}(a^{-x}b^{-x}c^{-x}+a^{-x}+ c^{-x})}[/math]
I have gotten up to this point:
[math]\frac{4}{1+ \frac{a^xb^x}{1+ b^xc^x}}+ b^{x}- \frac{4}{\frac{1}{b^{x}}(\frac{1}{a^{x}b^{x}c^{x}}+\frac{1}{a^{x}}+\frac{1}{c^{x}})}[/math]
The solution in the book is 4, but I'm not sure that is correct, can someone help?
[math]\frac{4}{a^{-x}+\frac{1}{b^{-x}+\frac{1}{c^{-x}}}} \div \frac{1}{a^{-x}+ \frac{1}{b^{-x}}}- \frac{4}{b^{-x}(a^{-x}b^{-x}c^{-x}+a^{-x}+ c^{-x})}[/math]
I have gotten up to this point:
[math]\frac{4}{1+ \frac{a^xb^x}{1+ b^xc^x}}+ b^{x}- \frac{4}{\frac{1}{b^{x}}(\frac{1}{a^{x}b^{x}c^{x}}+\frac{1}{a^{x}}+\frac{1}{c^{x}})}[/math]
The solution in the book is 4, but I'm not sure that is correct, can someone help?