Multiple choice

If $a=0$, then the equation $\displaystyle \frac{x-a-1}{x-a}=a +1-\displaystyle \frac{1}{x-a}$ has

  1. one root.

  2. two roots.

  3. many roots.

  4. no roots.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If a=0, the equation is (x-1)/x = 1 - 1/x. This simplifies to 1 - 1/x = 1 - 1/x, which is true for all x except x=0. Thus, there are infinitely many roots.

AI explanation

Substitute a = 0 into the given equation to get the fraction with numerator x minus 1 and denominator x equal to 1 minus the fraction with 1 as the numerator and x as the denominator. Multiplying the entire equation by x results in x minus 1 equaling x minus 1, which simplifies to 0 equals 0. Because this is an identity that holds true for all values of x except x equals 0, the equation has many roots. The result is many roots.

Keep practicing — related questions