simplify (7n)/(24n^3-64n^2)*(9n-24)/(7n)

1) Let's reduce:

\frac{7 n}{24 n^{3} - 64 n^{2}} \cdot \frac{9 n - 24}{7 n}

ⓘ To multiply fractions, multiply the numerators together and the denominators together:

\frac{7 n}{24 n^{3} - 64 n^{2}} \cdot \frac{9 n - 24}{7 n}

\frac{7 n \cdot (9 n - 24)}{(24 n^{3} - 64 n^{2}) \cdot 7 n}

\frac{7 n \cdot (9 n - 24)}{(24 n^{3} - 64 n^{2}) \cdot 7 n}

2) Let's factor in

ℝ

24 n^{3} - 64 n^{2}

This expression can be factorized into:

n^{2} \cdot (24 n - 64)

Let's factor in

ℝ

(24 n - 64)

We factor out

8

, the greatest common divisor of the coefficients:

24 n - 64

8 \cdot (3 n - 8)

Factor found:

3 n - 8

The fraction:

\frac{n}{n^{2}}

simplifies by the common factor:

n

into the new quotient:

\frac{1}{n}

\frac{7 \cdot (9 n - 24)}{7 \cdot 8 n \cdot (3 n - 8) \cdot n}

ⓘ Multiplying powers with the same base adds the exponents:

n \cdot n

n^{2}

ⅰ

7 \cdot 8

56

\frac{7 \cdot (9 n - 24)}{56 n^{2} \cdot (3 n - 8)}

We divide the numerator and denominator of

\frac{9 n - 24}{3 n - 8}

by the common factor:

n - \frac{8}{3}

, which gives the new fraction:

\frac{9}{3}

\frac{7 \cdot 9}{56 \cdot n^{2} \cdot 3}

ⅰ

7 \cdot 9

63

■

56 \cdot 3

(50 + 6) \cdot 3

50 \cdot 3 + 6 \cdot 3

150 + 18

168

\frac{63}{168 n^{2}}

The fraction:

\frac{63}{168}

simplifies by the common factor:

21

into the new quotient:

\frac{3}{8}

▶Simplified form:

\frac{3}{8 n^{2}}