SOLUTION: Give an example (other than the ones in the lecture or the text book) of a rational equation where the solution(s) makes the denominator equal to zero, and hence must be rejected;

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Give an example (other than the ones in the lecture or the text book) of a rational equation where the solution(s) makes the denominator equal to zero, and hence must be rejected;       Log On


   



Question 121043: Give an example (other than the ones in the lecture or the text book) of a rational equation where the solution(s) makes the denominator equal to zero, and hence must be rejected; i.e the solutions are extraneous solutions.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Sometimes with rational equations a solution results in a denominator+equal+to+zero. This solution+must+be rejected since division by zero is undefined.
If a denominator is comprised of a variable or a variable expression, consider the value or values that would make the denominator equal to zero and make a note excluding those values as solutions.
Example:
Solve the rational equation algebraically 1%2F3+%96+1%2Fx+=+5%2F6 ….note that a denominator is comprised of a variable x and x+%26%2361683%3B0
1%2F3+-+1%2Fx+=+5%2F6…….for denominators of 3,x, and 6, the LCM is 6x, so we will have:

6x%2A%281%2F3%29+-+6x%2A%281%2Fx%29+=+6x%285%2F6%29…….simplify
…….simplify
2x+-+6+=+5x…….
+-+6+=+5x+-+2x…….

+-+6+=+3x…….
+-+6%2F3+=+x…….
+-+2+=+x…….

x+=+-+2…….This solution must be rejected