Question

divide. \\(\frac{6x^7 + 4x^5}{2x^3}\\)

Explanation:

Step1: Split the fraction

We can split the fraction \(\frac{6x^{7}+4x^{5}}{2x^{3}}\) into two separate fractions: \(\frac{6x^{7}}{2x^{3}}+\frac{4x^{5}}{2x^{3}}\)

Step2: Simplify each fraction

For the first fraction \(\frac{6x^{7}}{2x^{3}}\), divide the coefficients and subtract the exponents of \(x\) (using the rule \(\frac{x^{m}}{x^{n}} = x^{m - n}\)): \(\frac{6}{2}x^{7-3}=3x^{4}\)
For the second fraction \(\frac{4x^{5}}{2x^{3}}\), divide the coefficients and subtract the exponents of \(x\): \(\frac{4}{2}x^{5 - 3}=2x^{2}\)

Answer:

\(3x^{4}+2x^{2}\)