user
simplify :\frac{x}{\:a}+\frac{b}{x}=0
alphonsio

Here's the simplified version of the equation for a0a \neq 0 and x0x \neq 0 :

x2+ab=0x^2 + ab = 0


To simplify the expression xa+bx=0\frac{x}{a} + \frac{b}{x} = 0, let's follow these steps:

  1. First, let's find a common denominator for the fractions. The common denominator for aa and xx is axax.

    xa+bx=0\frac{x}{a} + \frac{b}{x} = 0

    Rewrite each fraction with the common denominator:

    x2ax+abax=0\frac{x^2}{ax} + \frac{ab}{ax} = 0

  2. Combine the fractions over the common denominator:

    x2+abax=0\frac{x^2 + ab}{ax} = 0

  3. For the fraction to be zero, the numerator must be zero (since the denominator axax is not zero for a0a \neq 0 and x0x \neq 0 ).

    x2+ab=0x^2 + ab = 0

  4. Solve for xx:

    x2=abx^2 = -ab

    Taking the square root of both sides:

    x=±abx = \pm \sqrt{-ab}

  5. Note that ab\sqrt{-ab} is a complex number if abab is positive, since the square root of a negative number involves the imaginary unit ii.

Thus, the solution to the given equation is:

x=±abx = \pm \sqrt{-ab}

If abab is positive, then the solutions can be written in terms of imaginary numbers:

x=±iabx = \pm i\sqrt{ab}

Disclaimer

This chatbot (Alphonsio) provides automated responses generated by machine-learning algorithms and relies on the accuracy of the underlying language models. While this Chatbot is programmed to provide accurate and relevant information, its information may not always be exhaustive, accurate, up-to-date or tailored to individual circumstances. It is not a substitute for professional advice or consultation with qualified experts. This chatbots and its responses are intended for informational purposes only and should not be used for commercial or business purposes. The creators of this chatbot are not liable for any damages or losses incurred as a result of using the information provided. By using our website, you acknowledge and agree to these terms. The data you submit to this chatbot is used to improve our algorithms. Under no circumstances should you submit sensitive data such as, but not limited to, personal data or passwords. The data you submit could then be made public.