Given:
an equation is given as
[tex]\frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10}[/tex]
Find:
we have to solve the given equation.
Explanation:
We will solve the equation by taking LCM as following
[tex]\begin{gathered} \frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10} \\ \frac{x-10+x}{x(x-10)}=\frac{x-9}{x-10} \\ \frac{2x-10}{x-10}=\frac{x(x-9)}{x-10} \\ 2x-10=x^2-9x \\ x^2-9x-2x+10=0 \\ x^2-11x+10=0 \\ x^2-10x-x+10=0 \\ x(x-10)-1(x-10)=0 \\ (x-10)(x-1)=0 \\ x=1,10 \end{gathered}[/tex]
But the given equation is undefined for x = 10,
Therefore, x = 1 is the only solution of the given equation.
