We have to simplify the given expression:
[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y}[/tex]
Dividing the terms of the numerator by the given term of denominator individually, we get
= [tex]\frac{14x^5y^4}{7x^3y}+\frac{21x^3y^2}{7x^3y}[/tex]
By using the laws of exponent, [tex]a^m \div a^n = a^{m-n}[/tex], we get
= [tex]\frac{7 \times 2 x^5y^4} {7x^3y} + \frac{7 \times 3 x^3y^2}{7x^3y}[/tex]
= [tex]\frac{2 x^5y^4} {x^3y} + \frac{3 x^3y^2}{x^3y}[/tex]
= [tex]{2 x^{5-3}y^{4-1}} + 3 y^{2-1}[/tex]
= [tex]{2 x^{2}y^{3}} + 3 y[/tex]
Therefore, the simplification of the given expression is [tex]{2 x^{2}y^{3}} + 3 y[/tex].
So, Option 3 is the correct answer.
