Tell whether the given rational expression is proper or improper.
-$$\frac { x ^ { 2 } - 9 x + 20 } { \left( x ^ { 2 } - 11 x + 30 \right) ( x + 5 ) }$$
A) Improper
B) Proper

Question

Quizplus · Accepted Answer

A rational expression is proper if the degree of the numerator is less than the degree of the denominator. In this case, the numerator has a degree of 2, and the denominator, when fully expanded, will also have a leading term of degree 2 (since it's a product of two polynomials, the highest degree term will be $x^3$), making the degree of the denominator higher than the numerator. Therefore, the given expression is proper.

Tell Whether the Given Rational Expression Is Proper or Improper x2−9x+20(x2−11x+30)(x+5)\frac { x ^ { 2 } - 9 x + 20 } { \left( x ^ { 2 } - 11 x + 30 \right) ( x + 5 ) }(x2−11x+30)(x+5)x2−9x+20​

Tell Whether the Given Rational Expression Is Proper or Improper $\frac { x ^ { 2 } - 9 x + 20 } { \left( x ^ { 2 } - 11 x + 30 \right) ( x + 5 ) }$