I chose to do this because it’s the most recent thing I learned and I want to commit it to memory.

When you hear equations and algebraic you probably think of solving for x, and this is no different.

The main new thing (which isn’t that new) is having to get a common denominator to be able to collect like terms and simplify. If it ends up as a quadratic you do as before; factor, complete square, or use quadratic formula.

Since there will be restrictions if x is on the bottom, you will need to check your solutions. If a solution ends up being included in the restrictions, that solution is an extraneous solution. If all solutions are extraneous, there is no solution.

Multiplying everything by the common denominator will cancel out the fraction.

Looking at the equation in factored form above, the restrictions on x will be 4 and -4 since the denominator can’t equal 0.

Let’s do a quadratic example.

To find and cancel out the common denominator:

Now you just rearrange and factor, for which you have options. In this case I’ll just complete the square. To make it look simpler I also switched signs (multiply both sides by -1) to make x squared positive.

x=0 will not be permissible.