Did I simplify this correctly? Complex fractions have been giving me trouble. And I don't have an answer sheet for these. \[\Large\frac{1+\frac{4}{x}}{1-\frac{16}{x^2}} = \frac{\frac{x}{x}+\frac{4}{x}}{\frac{x^2}{x^2}-\frac{16}{x^2}} = \frac{\frac{x+4}{x}}{\frac{x^2-16}{x^2}} = \frac{\frac{x+4}{x}}{\frac{(x-4)(x+4)}{x^2}}\] \[ = \frac{x+4}{x} * \frac{x^2}{(x-4)(x+4)} = \frac{x}{x-4}\]
easiest way is probably to multiply top and bottom of the original expression by \[x^2\]
checks out
you will get \[\frac{x^2+4x}{x^2-16}\] as a first step, then factor and cancel
you have the correct answer !
Ah! Makes sense.
Seems good.
Thanks
btw if you want to be real fancy you can factor the original denominator as \[(1-\frac{4}{x})(1+\frac{4}{x})\] and cancel right away
you will get \[\frac{1}{1-\frac{4}{x}}\], then multiply top and bottom by x and be done
slick
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