Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²/2x + 6/
3х - 5/X +3

Option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.

A rational expression is the ratio of two polynomials. It looks like fractions that have variables in their denominators. A rational expression is considered simplified if there are no common factors in its numerator and denominator.

For the given situation,

The rational expression is

7x²/(2x + 6) ÷ (3х - 5)/(x +3)

⇒ [tex]\frac{\frac{7x^{2} }{2x+6} }{\frac{3x-5}{x+3} }[/tex]

In conversion of division to multiplication, we need to change the division sign to multiplication sign and reciprocal the rational expression for simplification.

⇒ [tex](\frac{7x^{2} }{2x+6} )(\frac{x+3}{3x-5} )[/tex]

⇒ [tex](\frac{7x^{2} }{2(x+3)} )(\frac{x+3}{3x-5} )[/tex]

⇒ [tex](\frac{7x^{2} }{2(1)} )(\frac{1}{3x-5} )[/tex]

⇒ [tex]\frac{7x^{2} }{6x-10}[/tex]

Hence we can conclude that option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.

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