What are the solutions to the following equation?
Math convention does not allow division by 0. When 0 appears in the denominator of an expression, then that expression is undefined. How does this convention affect equations that contain quadratic expressions? Consider the following:
What are the solutions to the following equation?
Notice a quadratic expression in the numerator. It is a good idea to simplify quadratic expressions by factoring, so factor this numerator as follows:
If either of the factors in the numerator is 0, then the entire expression becomes 0. Thus, the solutions to this equation are x = 3 or x = −4.
Note that making the denominator of the fraction equal to 0 would not make the entire expression equal to 0. Recall that if 0 appears in the denominator, the expression becomes undefined. Thus, x = 2 (which would make the denominator equal to 0) is not a solution to this equation. In fact, because setting x equal to 2 would make the denominator 0, the value 2 is not allowed: x cannot equal 2.
Solve for x:
