Need to find excluded value--algebra equation.

Question

I was given this equation: x/x+5 = 2/x+5 - 2/3 and told to find the excluded value. Could really use a helping hand! Thanks.

Answer 1

When solving an equation with different denominators, you need to first find the lowest common denominator (LCD).  The LCD is  3(x + 5).  Rewriting the equation using the LCD gives you

 

3x/ [3(x + 5)] = [6 - 2(x + 5)] / [3(x + 5)]

 

 

The excluded values are values of x that make the denominator zero.  That value is x=-5.

 

If you wanted to solve for x, simply equate the numerators and solve the equation. 

Answer 2

Excluded values are simply that: values that are excluded, or left out. These are values that will make the denominator of a rational expression equal to 0. Remember, you're not allowed to divide by 0, so these values are important to identify and exclude when solving.

 

First you must identify the function.

 

For example, in rational expressions, you can equate the denominator to to 0. This is necessary to find out at what values of x does the denominator become 0 and because the denominator cannot be zero the values of x that we get from equating the denominator to 0 are the excluded values for a rational expressions.

 

 

  x    =    2     -     2

x+5      x+5         3

 

1.) Set the denominate with x equal to 0.

 

x+5 = 5

 

2.) Solve.

 

x+5 = 0

   -5   -5

    x = -5

 

2.) Since the denominator will equal 0 when x=-5, then the excluded value is -5.