SOLUTION: are the rational expressions a-b/b-a and b-a/a-b ( I cant put them in fraction form on here) equivalent? Explain in detail why the are or why they are not equivalent. thank

Algebra ->  Expressions-with-variables -> SOLUTION: are the rational expressions a-b/b-a and b-a/a-b ( I cant put them in fraction form on here) equivalent? Explain in detail why the are or why they are not equivalent. thank      Log On


   

Question 1133937: are the rational expressions a-b/b-a and b-a/a-b ( I cant put them in fraction form on here) equivalent? Explain in detail why the are or why they are not equivalent. thankyou.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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are the rational expressions a-b/b-a and b-a/a-b ( I cant put them in fraction form on here) equivalent? Explain in detail why the are or why they are not equivalent. thankyou.
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%28a-b%29%2F%28b-a%29 versus %28b-a%29%2F%28a-b%29
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%28%28-1%29%2F%28-1%29%29%28%28a-b%29%2F%28b-a%29%29
%28b-a%29%2F%28a-b%29
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


%28a-b%29%2F%28b-a%29+=+%28a-b%29%2F%28-1%28a-b%29%29+=+1%2F-1+=+-1

%28b-a%29%2F%28a-b%29+=+%28-1%28a-b%29%29%2F%28a-b%29+=+-1%2F1+=+-1

YES: the two expressions have the same value.

If you go very far with algebra and higher mathematics, you will encounter numerous problems where you have an expression like (a-b)/(b-a). Learn to recognize that the two expressions are opposites of each other: (a-b) = -1(b-a); (b-a) = -1(a-b).