What is (3a^3-75a)/(a(a+5)(a+5)) ?

The solution to (3a^3-75a)/(a(a+5)(a+5)) is (3(a-5))/(a+5)

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simplify (3a^3-75a)/(a(a+5)(a+5))

simplify

\frac{3 a ^{3} - 75 a}{a ( a + 5 ) ( a + 5 )}

\frac{3 ( a - 5 )}{a + 5}

Solution steps

\frac{3 a ^{3} - 75 a}{a ( a + 5 ) ( a + 5 )}

Apply exponent rule:

aa = a^{2}

(a + 5) (a + 5) = (a + 5)^{2}

= \frac{3 a ^{3} - 75 a}{a ( a + 5 ) ^{2}}

Factor

3 a^{3} - 75 a : 3 a (a^{2} - 25)

= \frac{3 a ( a ^{2} - 25 )}{a ( a + 5 ) ^{2}}

Factor

a^{2} - 25 : (a + 5) (a - 5)

= \frac{3 a ( a + 5 ) ( a - 5 )}{a ( a + 5 ) ^{2}}

Cancel the common factor:

a

= \frac{3 ( a + 5 ) ( a - 5 )}{( a + 5 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(a + 5)^{2} = (a + 5) (a + 5)

= \frac{3 ( a + 5 ) ( a - 5 )}{( a + 5 ) ( a + 5 )}

Cancel the common factor:

a + 5

= \frac{3 ( a - 5 )}{a + 5}

\frac{343}{3}

36 n^{2} - 1

\frac{x ^{2} - 4}{x ^{2} - 6 x + 8}

sec^{4} (x) - sec^{2} (x)

(6 ab + 10) (7 a - 2 b)

What is (3a^3-75a)/(a(a+5)(a+5)) ?
The solution to (3a^3-75a)/(a(a+5)(a+5)) is (3(a-5))/(a+5)