Week 13 – Precalculus 11

Rational Equations

This week in math we learned about Rational equations.

A rational equation is very similar to a rational expression, where a rational expression has us simplifying for the lowest and simplest possible answer, but a rational equation has us solving for whatever variable is in the equation.

An example of a rational equation would be: \frac {x+1}{x+3} + \frac {5}{x} = \frac {x}{2x+6} We can’t really use the same methods for simplifying since there are three fractions along with the equals sign. So one of the methods which I use is to multiply every term by whatever is on the bottom of the fraction, to get rid of the fraction entirely making it easier to solve for x in this case. The steps would look like this: first I would multiply each term by the common denominator (which is (x+3) (x) (2)) (2)(x)(x+3)(\frac {x+1}{x+3}) + (\frac {5}{x}) (x)(2)(x+3) = (\frac {x}{2(x+3}) (x+3)(2)(x) during this step is where we would put the non-permissable values. In the first term the (x+3) that is being multiplied gets cancelled out and all that would remain is (2)(x)(x+1) for the second term the (x) that is multiplying gets cancelled out making a 1. finally for the 3rd term the (2) and the (x+3) get cancelled out making a 1. so the equation that reamains without multiplying yet would look like: (2)(x)(x+1) + (2)(x)(5) = (x)(x+1) and from here we would just solve for x.

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