Improper fraction?

Question

Why (x^2+3x-4)/(x-4)(x+2) is a improper fraction?Give answer with reasons.

Answer 1

A rational expression is considered "improper" when the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

In this case, combining the factors in the denominator (I'm assuming that both (x-4) and (x+2) are supposed to be in the denominator) gives x^2 -2x -8, which is a quadratic. Since both the numerator and denominator are quadratics, this expression qualifies as an improper rational expression.

EDITED TO ADD: In response to the other answerers below, there's a difference between the notion of "improper" for a purely numeric fraction (for instance, 8/3 and -5/5 are improper, 2/9 is not) and the notion of "improper" for a rational expression, which depends on the degrees of the polynomials and *not* what they might evaluate to numerically depending on the values of the variables.

See the link below for more info. Hope that helps!

Answer 2

This fraction is an improper fraction if x^2+3x-4 > (x-4)(x+2), that is if x^2+3x-4 > x^2-2x-8.
so, if 3x - 4 > -2x -8.
5x > -4
x > -4/5.

Therefore, the fraction is improper for all values of x greater than or equal to -4/5.

Answer 3

Compare with numbers: 8/2 is a improper fraction because it is indeed an integer number.

A fraction like that will be improper when, after simplifying, result in a polynomial function.

(x^2+3x-4)/((x-4)(x+2)) = (x+4)(x-1)/((x-4)(x-2)) and cannot be simplified... it is improper.

Answer 4

It is not an improper fraction except for certain values of x. As Prune suggested, you can find values for which it is improper. However, it does not have to be improper.

Answer 5

(x-4)(x+2)=x^2-2x-8

x^2-2x-8 )x^2+3x-4 (1
x^2-2x-8
------------
5x+4
therefore (x^2+3x-4)/(x-4)(x+2)=1+[(5x+4)/(x^2-2x-8)]
that is why. got it!

Answer 6

cause