What is (40n^2+64n)/(16n^3+112n^2+160n) ?

The solution to (40n^2+64n)/(16n^3+112n^2+160n) is (5n+8)/(2(n+2)(n+5))

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simplify (40n^2+64n)/(16n^3+112n^2+160n)

simplify

\frac{40 n ^{2} + 64 n}{16 n ^{3} + 112 n ^{2} + 160 n}

\frac{5 n + 8}{2 ( n + 2 ) ( n + 5 )}

Solution steps

\frac{40 n ^{2} + 64 n}{16 n ^{3} + 112 n ^{2} + 160 n}

Factor

40 n^{2} + 64 n : 8 n (5 n + 8)

= \frac{8 n ( 5 n + 8 )}{16 n ^{3} + 112 n ^{2} + 160 n}

Factor

16 n^{3} + 112 n^{2} + 160 n : 16 n (n + 2) (n + 5)

= \frac{8 n ( 5 n + 8 )}{16 n ( n + 2 ) ( n + 5 )}

Cancel the common factor:

n

= \frac{8 ( 5 n + 8 )}{16 ( n + 2 ) ( n + 5 )}

Factor the number:

16 = 8 \cdot 2

= \frac{8 ( 5 n + 8 )}{8 \cdot 2 ( n + 2 ) ( n + 5 )}

Cancel the common factor:

8

= \frac{5 n + 8}{2 ( n + 2 ) ( n + 5 )}

- 2 < x < 2

- 12 x^{2} + 12 x = 0

36 x^{2} + 16 x + 2 = 0

- \frac{4}{- 4}

15 r^{2} - 6 r - 3 = - 2 r

What is (40n^2+64n)/(16n^3+112n^2+160n) ?
The solution to (40n^2+64n)/(16n^3+112n^2+160n) is (5n+8)/(2(n+2)(n+5))