Question 1189170
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The expression is undefined wherever the denominator of any fraction is zero, BEFORE simplifying.  The given expression is<br>
{{{((3c/(c^2-25))((c-5)/(6c^2-3c)))/(2/(c+5))}}}<br>
Factor each denominator....<br>
{{{((3c/((c+5)(c-5)))((c-5)/((3)(c)(2c-1))))/(2/(c+5))}}}<br>
Oberve that the values of c that make any of the denominators equal to 0 are -5, 5, 0, and 1/2.<br>
To simplify, cancel the common factors 3, c, and (c-5) in the numerator of the complex fraction...<br>
{{{(1/((c+5)(2c-1)))/(2/(c+5))}}}<br>
... then "flip and multiply":<br>
{{{(1/((c+5)(2c-1)))*((c+5)/2) = 1/(2(2c-1)) = 1/(4c-2)}}}<br>
ANSWER: {{{((3c/(c^2-25))((c-5)/(6c^2-3c)))/(2/(c+5))}}} = {{{1/(4c-2)}}}; c not equal to -5, 5, 0, or 1/2<br>