Answer:
Step-by-step explanation:
[tex]\frac{1}{1-x^{a-b}}+\frac{1}{1-x^{b-a}}\\\\\frac{1}{1-x^{b-a}}=\frac{1}{1-x^{-(a-b)}}=\frac{1}{1-\frac{1}{x^{a-b}}}\\=\frac{1}{\frac{x^(a-b)-1}{x^(a-b)}}=\frac{x^{a-b}}{x^{a-b}-1}\\\\=\frac{x^{a-b}}{-(1-x^{a-b})}=-\frac{x^{a-b}}{1-x^{a-b}}\\\\\frac{1}{1-x^{a-b}}+\frac{1}{1-x^{b-a}}=\frac{1}{1-x^{a-b}}-\frac{x^{a-b}}{1-x^{a-b}}\\\\=\frac{1-x^{a-b}}{1-x^{a-b}}=1[/tex]
