Answer:
The value of x = 4/7
Step-by-step explanation:
Given the expression
[tex]\frac{4}{7\left(x+6\right)}=\frac{x}{x+6}[/tex]
[tex]\frac{4}{7\left(x+6\right)}-\frac{x}{x+6}=0[/tex]
Multiply the numerator and denominator of [tex]\frac{x}{x+6}[/tex] by 7
[tex]\frac{4}{7\left(x+6\right)}-\frac{7x}{7\left(x+6\right)}=0[/tex]
Now taking the denominator [tex]\frac{1}{7\left(x+6\right)}[/tex] as common
[tex]\frac{1}{7\left(x+6\right)}\left(4-7x\right)=0[/tex]
[tex]\frac{4-7x}{7\left(x+6\right)}=0[/tex]
[tex]\frac{f\left(x\right)}{g\left(x\right)}=0\quad \Rightarrow \quad f\left(x\right)=0[/tex]
[tex]4-7x=0[/tex]
Subtract 4 from both sides
[tex]4-7x-4=0-4[/tex]
Simplify
[tex]-7x=-4[/tex]
Divide both sides by -7
[tex]\frac{-7x}{-7}=\frac{-4}{-7}[/tex]
Simplify
[tex]x=\frac{4}{7}[/tex]
Therefore,
The value of x = 4/7
