The solution is [tex]x=14[/tex]
Explanation:
The given expression is [tex]\frac{6}{x^{2} -3x}=\frac{1}{x}- \frac{5}{x^{2} -3x}[/tex]
We need to determine the solution of the expression.
Let us simplify the equation by taking LCM on both sides.
The LCM of [tex]x^{2} -3x[/tex] is [tex]x(x-3)[/tex]
Thus, we have,
[tex]\frac{6}{x^{2} -3x}x(x-3)=\frac{1}{x}x(x-3)- \frac{5}{x^{2} -3x}x(x-3)[/tex]
Simplifying the terms, we get,
[tex]6=x-3-5[/tex]
Subtracting the terms, we have,
[tex]6=x-8[/tex]
Subtracting both sides of the expression by 6, we get,
[tex]0=x-14[/tex]
Adding both sides of the expression by 14, we have,
[tex]14=x[/tex]
Thus, the solution of the equation is [tex]x=14[/tex]
