Solve : 1/1-x^a-b + 1/1-x^b-a

The answer to the above eqaution is 1

Step-by-step explanation:

Proceeding step by step

Step 1 = 1 / (1-xᵃ⁻ᵇ) + 1 / (1-xᵇ⁻ᵃ)

on rearranging the equation (b-a) as - (a-b) and substituting the value

Step 2 = 1 / (1-x ᵃ⁻ᵇ) + 1 / (1-x - ⁽ᵃ⁻ᵇ⁾)

Using the indices corrolary that 1/1 - x ⁻ᵃ = - xᵃ / (1 - x ᵃ) and subsituting the value of the expression in the step mentioned below

Step 3=1 / (1+x ᵃ⁻ᵇ) - (x ᵃ⁻ᵇ) / (1-x ᵃ⁻ᵇ)

Since the denominators are the same the two fractions can be added with common denominator being 1+x ᵃ⁻ᵇ

On adding the above mentioned step 3 we get

Step 4 = (1 - x ᵃ⁻ᵇ) / (1 - x ᵃ⁻ᵇ)

=1

Thus the value of equation = 1