Question

SImplify:

(x - 9/x) / (1 + x/3)



and (m^-1 + n^-1) / (m^-3 + n^-3)

I have no idea what to do

Answer 1

Answer to #2:

m^4n^2.

I subtracted the m's and subtracted the m's. It's one of the exponent rules.

I have NO idea how to do the first question.

Answer 2

you cant do that, Miley, the m's and n's are separated by an addition sign, so you cant use the quotient of powers rule

Answer 3

oh okay sry, at least i tried

Answer 4

for the first one, just multiply them using FOIL
to get

x + (x^2)/3 - 9/x - 3

for the second, use the rule for negative exponents to write

(1/m + 1/n)/(1/m^3 + 1/n^3)

finding common denominators and simplifying both top and bottom I got

(m+n)/mn / (m^3 + n^3)/m^3n^3
= (m+n)/mn * (m^3n^3)/(m^3 + n^3)
= m^2n^2(m+n) / (m^3 + n^3)

the bottom factors to (m+n)(m^2 - mn + n^2)

so we have
m^2n^2(m+n) / ((m+n)(m^2 - mn + n^2))
= m^2n^2 / (m^2 - mn + n^2)