Simplify each of the following fractions 1a)2/x4 1b)3x+9/x+5 1c) 14x^3-x^2+9x-2/x^2-16 1d)3x/6x^2-x-2

 2.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  x2  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 3.1     Pull out like factors :

   x2 + x  =   x • (x + 1) 

 3.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 4.1   Adding a whole to a fraction 

Rewrite the whole as a fraction using  x2  as the denominator :

answer: -1

step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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