Question

Rewrite the rational expressions x³+x²-7/x-3A) x²+4x+12+29A) x²+4x+12+29/x-3A) x²+4x+12+19/x-3A) x²+3x+12

Answer 1

We have the expression:

`(x^3+x^2-7)/(x-3)`

We can simplify it by dividing the numerator by the denominator (division of polynomials):

`\begin{gathered} (x^3+x^2-7)/(x-3) \\ (x^3-3x^2+3x^2+x^2-7)/(x-3)=(x^2(x-3))/(x-3)+(4x^2-7)/(x-3)=x^2+(4x^2-7)/(x-3) \\ x^2+(4x^2-12x)/(x-3)+(12x-7)/(x-3)=x^2+(4x(x-3))/(x-3)+(12x-7)/(x-3)=x^2+4x+(12x-7)/(x-3) \\ x^2+4x+(12x-36)/(x-3)+(36-7)/(x-3)=x^2+4x+(12(x-3))/(x-3)+(29)/(x-3) \\ x^2+4x+12+(29)/(x-3) \end{gathered}`

The answer is: x²+4x+12+29/(x-3)