Multiple choice

The roots of the equation $\dfrac{a}{x+a}+\dfrac{b}{x+b}=1$ are:

  1. $\pm ab$
  2. $\pm \sqrt{ab}$
  3. $\pm (a+b)$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

a/(x+a) + b/(x+b) = 1. Multiply by (x+a)(x+b): a(x+b) + b(x+a) = (x+a)(x+b). ax+ab + bx+ab = x^2 + ax + bx + ab. Simplifying gives x^2 = ab, so x = +/- sqrt(ab).

AI explanation

Multiply the equation a/(x+a)+b/(x+b)=1 by the common denominator (x+a)(x+b) to clear the fractions. This gives a(x+b)+b(x+a)=(x+a)(x+b). Expanding both sides produces ax+ab+bx+ab=x^2+ax+bx+ab. Simplifying this yields x^2=ab. Taking the square root of both sides gives the roots as the positive and negative square root of ab.

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