Given:
The equation is:
[tex]x+\frac{6}{x}=-7[/tex]Find-:
Restrictions for this equation
Explanation:
The equation is:
[tex]\begin{gathered} x+\frac{6}{x}=-7 \\ \\ \frac{x^2+6}{x}=-7 \end{gathered}[/tex]The denominator is not equal to zero. If the denominator is zero, then the function is undefined.
Then the restriction is:
[tex]x\ne0[/tex]For the function value of x is:
[tex]\begin{gathered} \frac{x^2+6}{x}=-7 \\ \\ x^2+6=-7x \\ \\ x^2+7x+6=0 \\ \end{gathered}[/tex]The value of "x" is:
[tex]\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}[/tex]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
[tex][/tex]