how to solve the equation x(x+2 ) / x+2=x

Question

x(x+2) / x+2=x

 

Answer 1

Hi Jeanetta:

 

An equation is a statement.  The challenge is to find what value or values of X will make the statement true.  For curiosity what if you substituted the value of 2 for X in the equation.  What then will the statement say?

 

First, however, it is important to understand the ORDER of operations and understand that the +2 at the end of the left expression is done last.

 

x(x+2)/x   +2  = X.

 

The left expression simplifies to X+4 as X/X = 1 for all X

 

That leaves X+2     + 2  = X or 6=2???  Clearly, this is a false statement so X=2 cannot be a solution.

 

Try other values of X and notice that just about everyone you try will result in a false statement.

 

However, since X/X = 1 then the left side simplifies to X +4 thus the equation states X+4 = X

 

Clearly this cannot be true under any values of X thus there is no solution!

 

Without noticing the order of operations one could easily write the statement this way:

 

X(X+2)/(X+2) = X.  In this way, you can see that all values of X will satisfy this equation as it clearly states X=X