Question

\frac{16a^{4}-40a^{2}+24a}{12a^{3}}

Explanation:

Step1: Factor numerator and denominator

First, factor out the greatest common factor (GCF) from the numerator and the denominator. The GCF of \(16a^4\), \(-40a^2\), \(24a\) and \(12a^3\) is \(4a\).
For the numerator: \(16a^4 - 40a^2 + 24a=4a(4a^3 - 10a + 6)\)
For the denominator: \(12a^3 = 4a\times3a^2\)

Step2: Cancel out common factors

Now, cancel out the common factor \(4a\) from the numerator and the denominator.
\(\frac{4a(4a^3 - 10a + 6)}{4a\times3a^2}=\frac{4a^3 - 10a + 6}{3a^2}\)

We can also split the fraction:
\(\frac{4a^3}{3a^2}-\frac{10a}{3a^2}+\frac{6}{3a^2}\)

Step3: Simplify each term

Simplify each term using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) (\(a
eq0\)):

• For the first term \(\frac{4a^3}{3a^2}=\frac{4}{3}a^{3 - 2}=\frac{4}{3}a\)
• For the second term \(\frac{- 10a}{3a^2}=\frac{-10}{3}a^{1-2}=\frac{-10}{3a}\)
• For the third term \(\frac{6}{3a^2}=\frac{2}{a^2}\)

So the simplified form is \(\frac{4}{3}a-\frac{10}{3a}+\frac{2}{a^2}\) or \(\frac{4a^3 - 10a + 6}{3a^2}\)

Answer:

\(\frac{4a^3 - 10a + 6}{3a^2}\) (or \(\frac{4}{3}a-\frac{10}{3a}+\frac{2}{a^2}\))