Solve for x.
\dfrac{TERM1}{x - NUMERATOR}
= \dfrac{TERM2}{x - NUMERATOR}
x = a x = a
x = NUMERATOR.x = A.x = B.What is the extraneous solution to this equation?
\dfrac{TERM1}{x - NUMERATOR}
= \dfrac{TERM2}{x - NUMERATOR}
At x = NUMERATOR, the denominator of the original expression is 0.
Since the expression is undefined at x = NUMERATOR, it is an extraneous solution.
x = A and x = B, so there are no extraneous solutions.Multiply both sides by x - NUMERATOR:
\qquad \dfrac{TERM1}{x - NUMERATOR} (x - NUMERATOR)
= \dfrac{TERM2}{x - NUMERATOR} (x - NUMERATOR)
\qquad TERM1 = TERM2
Subtract TERM2 from both sides:
\qquad TERM1 - (TERM2) = TERM2 - (TERM2)
\qquad TERM1 + TERM2NEG = 0
\qquad TERM1.add(TERM2NEG) = 0
Factor the expression:
\qquad (x - A)(x - B) = 0
Therefore x = A or x = B