rational expression
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

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.

 

by Top Rated User (841k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,327 questions
92,381 answers
2,254 comments
23,935 users