Question

Given this equation, what would the restriction be?X+6/x= -7

Answer 1

Given:

The equation is:

`x+(6)/(x)=-7`

Find-:

Restrictions for this equation

Step-by-step explanation:

The equation is:

`\begin{gathered} x+(6)/(x)=-7 \\ \\ (x^2+6)/(x)=-7 \end{gathered}`

The denominator is not equal to zero. If the denominator is zero, then the function is undefined.

Then the restriction is:

`x\\e0`

For the function value of x is:

`\begin{gathered} (x^2+6)/(x)=-7 \\ \\ x^2+6=-7x \\ \\ x^2+7x+6=0 \\ \end{gathered}`

The value of "x" is:

`\begin{gathered} x^2+6x+x+6=0 \\ \\ x(x+6)+1(x+6)=0 \\ \\ (x+6)(x+1)=0 \\ \\ x=-6\text{ and }x=-1 \end{gathered}`

So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1