Question

The following rational equation has denominators that contain variables. for this equation,

A. write the value or values of the variable that makes the denominator zero. These are the restrictions on the variable. B. keeping the restrictions in mind, solve the equation.
3/x+4 + 2/x-4 = 16/(x+4)(x-4)

Answer 1

A. x ≠ -4 or +4

B. no solution

Explanation:

You want the restrictions on x and the solution to the equation ...

3/(x+4) +2/(x-4) = 16/((x +4)(x -4))

A. Restrictions

The denominator factors are (x+4) and (x-4). The values of x that make these zero are -4 and +4, respectively.

The variable may not have values -4 or +4.

B. Solution

In order to avoid extraneous solutions, it often works well to rewrite the equation in the form f(x) = 0. We can subtract 16/((x+4)(x-4)) from both sides to make that happen.

`(3)/(x+4)+(2)/(x-4)-(16)/((x+4)(x-4))=0\\\\\\(3(x-4)+2(x+4)-16)/((x+4)(x-4))=0\\\\\\(5x-20)/((x+4)(x-4))=(5(x-4))/((x+4)(x-4))=(5)/(x+4)=0`

There is no value of x that will make this true. The equation has no solution.