Question 172176
Is the expression {{{(1-((2-1/x)/x))/(1-1/x)}}} ???



{{{(1-((2-1/x)/x))/(1-1/x)}}} Start with the given expression



{{{(1-(((2x)/(x)-1/x)/x))/(1-1/x)}}} Multiply 2 by {{{x/x}}}



{{{(1-((2x-1)/x)/x)/(1-1/x)}}} Combine {{{(2x)/(x)-1/x}}} to get {{{(2x-1)/x}}}




{{{(1-(2x-1)/(x^2))/(1-1/x)}}} Simplify {{{((2x-1)/x)/x}}} to get {{{((2x-1)/x)*(1/x)=(2x-1)/(x^2)}}}




{{{(1*x^2-cross(x^2)((2x-1)/cross(x^2)))/(1*x^2-x^2*(1/cross(x)))}}} Multiply EVERY term by the inner LCD {{{x^2}}} to clear the inner fractions.



{{{(x^2-(2x-1))/(x^2-x)}}} Simplify



{{{(x^2-2x+1)/(x^2-x)}}} Distribute



{{{((x-1)(x-1))/(x^2-x)}}} Factor the numerator



{{{((x-1)(x-1))/(x(x-1))}}} Factor the denominator



{{{(highlight((x-1))(x-1))/(x*highlight((x-1)))}}} Highlight the common terms.



{{{(cross((x-1))(x-1))/(x*cross((x-1)))}}} Cancel out the common terms.



{{{(x-1)/x}}} Simplify




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Answer:


So {{{(1-((2-1/x)/x))/(1-1/x)}}} simplifies to {{{(x-1)/x}}}