algebraic continuity theorem

[BMAD]

I am helping a friend in introductory real analysis, someone please help me finish, I am stuck.

Want to show that f(x)/g(x) is continuous as x goes to c given that g© is not 0.

|f(x)/g(x) - f©/g©| = |1/(g(x)g©)||f(x)g©-f©g(x)| = |1/(g(x)g©)||f(x)g©-f©g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g©)||f(x)||g(x)-g©| + |g(x)||f(x)- f©|

Then I draw a Blank.

[BMAD]

Found my mistake !

[bonanova]

Hi BMAD,

Hint, to keep ( c ) from turning into © you can insert spaces, or use [c] as a substitute.

Are there others?

(a) (b) © (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) ® (s) (t) (u) (v) (w) (x) (y) (z)

( c ) ( r )

[BMAD]

I appreciate it.

[aliceklein]

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