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Solving rational equations

Solving rational equations. Using the method that focuses on numerators only. Example – Solve for x. Look at all of the denominators. We want to multiply each fraction by something so that they will all have the same exact denominator. In this case, the LCD is 6x^2.

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Solving rational equations

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  1. Solving rational equations Using the method that focuses on numerators only

  2. Example – Solve for x Look at all of the denominators. We want to multiply each fraction by something so that they will all have the same exact denominator In this case, the LCD is 6x^2 The method we will use in these problems requires us to find an LCD Now that they all have the same denominator, we only need to work with the numerators. Anytime you have a squared term (or higher power) you should ALWAYS GET 0 ON ONE SIDE OF YOUR EQUATION We now have a quadratic equation

  3. We can either solve this by factoring or by using the quadratic formula. Factoring is shown first here. OR OR The check is left to you (both solutions check).

  4. Here, we’ll use the quadratic formula to solve that last problem. The quadratic formula is Therefore Or Or

  5. The most difficult part of these problems is identifying the LCD. Take this one for example: Solve for x Be careful: The LCD here is NOT z-1. We cannot multiply z by anything so that it becomes z – 1, so our LCD is z(z-1) Final answer

  6. Solve for x Factor to find the LCD

  7. Check youtube or google for more practice problems with solutions. Or you can come to SGI if you don’t understand any of these problems or any other problems.

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