# 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.