Question

How do you simplify `(a^-1+b^-1)/(a^-2+b^-2)`?

Answer 1

`(ab(a+b))/(a^2+b^2)`

Explanation:

Write the terms as fractions and then add them.

`(a^-1+b^-1)/(a^-2+b^-2) " = "(1/a + 1/b)/((1/a^2 + 1/b^2)`

Find common denominators and make equivalent fractions:

`((b+a)/(ab))/((b^2+a^2)/(a^2b^2))color(white)(xxxxxxxxxxx)rarr (a/b)/(c/d) = (axxd)/(bxxc)`

= `((b+a)xx(a^2b^2))/((ab)(b^2+a^2))`

=`(ab(a+b))/(a^2+b^2)`