# Removing the Demonimator by Multiplying Both Sides By LCD

When we solve a rational equation, why is it OK to remove the denominator by multiplying both sides by the LCD? Why can you not remove the denominator when simplifying a rational expression? Provide examples to support your discussion.

2. What are extraneous solutions of an equation? Why do they sometimes occur when we solve rational or radical equations? Provide examples to support your discussion.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/removing-demonimator-multiplying-sides-lcd-31957

#### Solution Preview

Please see attached file.

(a) If you multiply both sides of an equation by a non-zero number, the equality is still preserved. For example, we know that 2 = 2. If we multiply both sides by 3, we get 6 = 6 (which is quite ...

#### Solution Summary

The solution discusses why when solving a rational equation, it is OK to remove the denominator by multiplying both sides by the LCD.