mathwithhotti

Solving an equation containing two radicals

In our next example, we are going to solve an equation that contains two radicals.  No matter what we do, we must always try to isolate the radical before we start to solve the equation.  It does not make a difference which radical you isolate, but isolate one of them.  Once the radical is isolated, we can square both sides of our equation.  Combine like terms.  Notice we still have a radical left over.  Isolate that radical now.  Once that radical is isolated, square both sides of the equation again.  Then we can solve the resulting quadratic equation.

Solving an equation containing a radical

In like our next like example, like we are like going to like solve a radical equation.  Oh, sorry about that.  Let's try that again. In our next example, we are going to solve an equation that contains a radical.  No matter what we do, we must always try to isolate the radical before we start to solve the equation.  Once the radical is isolated, we can square both sides of our equation.  Solve the resulting equation whether it is a simple linear equation or a quadratic equation.

Simplifying a complex fraction

Some think that fractions are complex enough.  But when there is a fraction within a fraction, it really gets complex.  To make the problem easier, multiply both the numberator and denominator by the least common multiple to get rid of the fractions within the fractions.  You might need to factor and reduce when you are done.

Solving an equation with variables in the denominator #2

In this example, we solve an equation with fractions but with varibles in the denominator.  If you do not like to work with fractions, find the least common multiple of the denominator.  Then multiply each term by the least common multiple and voila the fractions are gone and you can solve the equation that is left. We will need to check to see if our answer is extraneous.  Plug the solutions into the original equation and check to see if zero is produced in the denominator.  If so, then the solution is extraneous.  Only put solutions that are not extraneous in your solution set.

Solving an equation with variables in the denominator

In this example, we solve an equation with fractions but with variables in the denominator.  If you do not like to work with fractions, find the least common multiple of the denominator.  Then multiply each term by the least common multiple and voila the fractions are gone and you can solve the equation that is left. We do need to check our solution as it could be extraneous, a solution that does not work in the original problem.  Why?  Well, we know that in a fraction, the denominator can not be zero.  We cannot divide by zero as there is no reciprocal for zero.