Question 146061
{{{(1-(y^2)/(x^2))/(1-(y)/(x))}}} Start with the given expression



{{{(x^2(1-(y^2)/(x^2)))/(x^2(1-(y)/(x)))}}} Multiply <b>both</b> numerator and denominator by the LCD {{{x^2}}}



{{{(x^2-y^2)/(x^2-xy)}}} Distribute. Notice how the inner denominators cancel.



{{{((x+y)(x-y))/(x^2-xy)}}} Factor the numerator.



{{{((x+y)(x-y))/(x(x-y))}}} Factor the denominator.



{{{((x+y)cross((x-y)))/(x*cross((x-y)))}}} Cancel like terms.



{{{(x+y)/x}}} Simplify.




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