Asked by Jessica
Please solve and check all proposed solutions. Show work for solving and checking:
(x-2)/(x-1) + (2)/(x^2-1) = 0
(x-2)/(x-1) + (2)/(x^2-1) = 0
Answers
Answered by
MathMate
(x-2)/(x-1) + (2)/(x^2-1) = 0
(x-2)/(x-1) + (2)/((x-1)(x+1)) = 0
Take out the common factor 1/(x-1)
(1/(x-1)((x-2)+2/(x+1)) = 0
Solve for (x-2)+2/(x+1) = 0
to give x=0;
The common factor of 1/(x-1) tells us that x=1 is NOT a solution, because it would make the expression on the left side indefinite.
Another way to do the problem is to transpose one of the terms to the right-hand-side and cross multiply. Solve the resulting equation to get 0 and 1 as roots. Reject 1 as a root when back-substituted into the original equation gives infinite values.
(x-2)/(x-1) + (2)/((x-1)(x+1)) = 0
Take out the common factor 1/(x-1)
(1/(x-1)((x-2)+2/(x+1)) = 0
Solve for (x-2)+2/(x+1) = 0
to give x=0;
The common factor of 1/(x-1) tells us that x=1 is NOT a solution, because it would make the expression on the left side indefinite.
Another way to do the problem is to transpose one of the terms to the right-hand-side and cross multiply. Solve the resulting equation to get 0 and 1 as roots. Reject 1 as a root when back-substituted into the original equation gives infinite values.
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