Combining two fractions involing powers of x

Question

Is there any way i can write

$x^a+x^b$ as d$x^c$

Im considering writing letting $a=a-1$ and partial fractions but im getting really confused.

Answer 1

It is (near) never true: $x^a+x^b=x^a(1+x^{b-a})$ and the expression in the parentheses is not of the form $Ax^E$, because limit in the infinity shows that $A=1$, $E=b-a$, but then, e.g. for $x=0$, the expressions are different.