For non-zero denominators, simplify:
\[ \frac{3a^3-75a}{a(a+5)(a+5)} \]
Answer (2)
a ( a + 5 ) ( a + 5 ) 3 a 3 − 75 a = a ( a + 5 ) ( a + 5 ) 3 a ( a 2 − 25 ) = a ( a + 5 ) ( a + 5 ) 3 a ( a − 5 ) ( a + 5 ) = ( a + 5 ) 3 ( a − 5 )
To simplify a ( a + 5 ) ( a + 5 ) 3 a 3 − 75 a , we factor the numerator to get a ( a + 5 ) ( a + 5 ) 3 a ( a − 5 ) ( a + 5 ) and cancel the common factors. The simplified form is 3 ( a − 5 ) , valid for a = 0 and a = − 5 .
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