Simplify the following algebraic expressions: (a3+1)/(a2-a+1) + (a3-1)/(a2+a+1) and (m2+mn+n2)/(m+n)…

Question

Simplify the following algebraic expressions: (a3+1)/(a2-a+1) + (a3-1)/(a2+a+1) and (m2+mn+n2)/(m+n) + (m2-mn+n2)/(m-n)

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

:

\frac{a^3+1}{a^2-a+1} + \frac{a^3-1}{a^2+a+1}

Factor the numerators using the sum and difference of cubes formulas, $x^3+y^3 = (x+y)(x^2-xy+y^2)$ and $x^3-y^3 = (x-y)(x^2+xy+y^2)$ .
$a^3+1 = (a+1)(a^2-a+1)$ $a^3-1 = (a-1)(a^2+a+1)$
Substitute the factored forms into the expression.
$\frac{(a+1)(a^2-a+1)}{a^2-a+1} + \frac{(a-1)(a^2+a+1)}{a^2+a+1}$
Cancel out common terms in the numerators and denominators.
$(a+1) + (a-1)$
Simplify the expression.
$a+1+a-1 = 2a$
The final answer is $\boxed{2a}$ .

:
$\frac{m^2+mn+n^2}{m+n} + \frac{m^2-mn+n^2}{m-n}$
Find a common

Simplify the following algebraic expressions: (a3+1)/(a2-a+1) + (a3-1)/(a2+a+1) and (m2+mn+n2)/(m+n) + (m2-mn+n2)/(m-n)