Answer:
X = -3. non-extraneous
Step-by-step explanation:
The given equation is [tex]\frac{6}{x-3} =\frac{x}{3}[/tex]
We cross multiply to get:
[tex]6*3=x(x-3)[/tex]
Expand and multiply.
[tex]18=x^2-3x[/tex]
[tex]x^2-3x-18=0[/tex]
We factor to obtain:
[tex](x-6)(x+3)=0[/tex]
[tex]x=-3,x=6[/tex]
Checking for extraneous solutions
Substitute x=-3 [tex]\frac{6}{-3-3} =\frac{-3}{3}[/tex]
[tex]\frac{6}{-6} =\frac{-3}{3}[/tex]
[tex]-1=-1[/tex]
[tex]1=1[/tex].....Non-extraneous
Checking for x=6
[tex]\frac{6}{6-3} =\frac{6}{3}[/tex]
[tex]\frac{6}{3} =\frac{6}{3}[/tex]
[tex]2=2[/tex]....Non-extraneous
