Question 198578
Is the expression {{{(1/5-1/y)/(5-y/5)}}}???



{{{(1/5-1/y)/(5-y/5)}}} Start with the given expression.



{{{((1/cross(5))cross(5)*y-(1/cross(y))5*cross(y))/(5*5y-(y/cross(5))cross(5)*y5)}}} Multiply EVERY term by the inner LCD 5y to clear out the inner fractions.



{{{(1*y-1*5)/(5*5y-y*y)}}} Simplify



{{{(y-5)/(25y-y^2)}}} Multiply




So {{{(1/5-1/y)/(5-y/5)=(y-5)/(25y-y^2)}}}



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OR...


Is the expression {{{(1/5-1/y)/((5-y)/5)}}} ???




{{{(1/5-1/y)/((5-y)/5)}}} Start with the given expression.



{{{((1/cross(5))cross(5)*y-(1/cross(y))5*cross(y))/(((5-y)/cross(5))cross(5)*y)}}} Multiply EVERY term by the inner LCD 5y to clear out the inner fractions.



{{{(1*y-1*5)/(y(5-y))}}} Simplify



{{{(y-5)/(y(5-y))}}} Multiply



{{{(y-5)/(-y(y-5))}}} Factor the denominator



{{{-(y-5)/(y(y-5))}}} Reduce



{{{-cross((y-5))/(y*cross((y-5)))}}} Cancel out the common terms.



{{{-1/y}}} Simplify



So {{{(1/5-1/y)/((5-y)/5)=-1/y}}}