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Pasha
Mathematics
12 December, 18:23
Solve : 1/1-x^a-b + 1/1-x^b-a
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Tatiana Dalton
12 December, 18:41
0
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
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