Question

Simplify: (1/(x+4)) + (1/(x-4))
Show work please! Thanks:)

Answer 1

Okay, so we could try writing everything in the same fraction and see if that simplifies it:
\[ \frac{1}{x+4}+\frac{1}{x-4} = \frac{x-4}{(x+4)(x-4)}+\frac{x+4}{(x-4)(x+4)} \\=
\frac{(x-4)+(x+4)}{(x+4)(x-4)} = \frac{x+x+4-4}{x^2-4^2} = \frac{2x}{x^2-16}
\]
I think it did.

Answer 2

\[\frac{(x-4)+x+4)}{(x-4)(x+4)}=\frac{2x}{(x-4)(x+4)}\]

Answer 3

In general to combine two fractions you would do:
\[ \frac{a}{b}+\frac{c}{d} = \frac{a*d}{b*d}+\frac{c*b}{d*b} = \frac{a*d+c*b}{b*d} \]
Or in english: extend each fraction with the other fractions denominator.

Answer 4

Thanks for the info dape! Usually no one or barely anyone helps on here.

Answer 5

No problem, glad you found it helpful =)