rational expression

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## 1 Answer

Call the fraction (d-2)/d=1-2/d. 1 1/5=6/5=1.2. The fraction is inverted to d/(d-2) when 6/5 is added:

(d-2)/d+6/5=d/(d-2). Multiply through by 5d(d-2):

5(d-2)^2+6d(d-2)=5d^2.

5d^2-20d+20+6d^2-12d=5d^2.

6d^2-32d+20=0, 3d^2-16d+10=0

d=(16±√(256-120))/6=(8±√34)/3 which is irrational.

So d=(8+√34)/3 or (8-√34)/3 and d=4.6103 or 0.7230.

The fraction is (d-2)/d=(2+√34)/3÷(8+√34)/3=(2+√34)/(8+√34)=(2+√34)(8-√34)/(64-34)=(16+6√34-34)/30=(√34-3)/5 when rationalised. d=0.7230 is rejected because d-2 would be negative and the fraction must be positive.

CHECK

(√34-3)/5+6/5=(3+√34)/5; (3+√34)/5 * (√34-3)/5=(34-9)/25=25/25=1, so the fraction has been inverted because a fraction multiplied by its inverse is 1.

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