(-x_(1)(-1))/((1-x)(-1))-(x)/(x-1) Rightarrow (-x)/(1-x)=(x)/(x-1) 6.7: ( a) ) ((x-2)^2(x-2))/(x(x-2))-((x-2)^2)/(x) ( b) ) (-(x-1))/(-(5 x-1))=(x-1)/(5 x-1)

The given equation is $\frac {(x-2)^{2}(x-2)-(x-2)^{2}}{x(x-2)}=\frac {(x-2)^{2}}{x}$. To solve this equation, we first simplify the numerator of the left-hand side. We can factor out $(x-2)^2$ from the numerator, which gives us $\frac {(x-2)^2[(x-2)-(x-2)]}{x(x-2)}$. This simplifies further to $\frac {(x-2)^2[0]}{x(x-2)}$, which is equal to 0. Therefore, the left-hand side of the equation simplifies to 0. The right-hand side of the equation is $\frac {(x-2)^{2}}{x}$, which is not equal to 0 for any value of x except when x is 2. Therefore, the given equation has no solution.