aangenaamyj

Answered

2022-07-15

I've actually struggled with how to properly simplify this rational function, and I'm hoping someone can point me in the right direction. It's part of my precalculus class/section on graphing rational functions by translation:

$f(x)=\frac{-x}{7x+5}$

I can get along OK with simpler such rational functions, but this one is throwing me for a loop, because of the (-x) in the numerator.

Any help is greatly appreciated! I'm sorry for any formatting problems in advance, as I'm new to this site.

$f(x)=\frac{-x}{7x+5}$

I can get along OK with simpler such rational functions, but this one is throwing me for a loop, because of the (-x) in the numerator.

Any help is greatly appreciated! I'm sorry for any formatting problems in advance, as I'm new to this site.

Answer & Explanation

Caiden Barrett

Expert

2022-07-16Added 20 answers

Find an equivalent form which you can already graph by translations:

$f(x)=\frac{-x}{7x+5}=\text{}-\frac{x+5/7}{7x+5}\text{}+\frac{5/7}{7x+5}\text{}=\phantom{\rule{0ex}{0ex}}=-\frac{1}{7}\text{}+\frac{5}{49x+35}\phantom{\rule{thinmathspace}{0ex}}.$

$f(x)=\frac{-x}{7x+5}=\text{}-\frac{x+5/7}{7x+5}\text{}+\frac{5/7}{7x+5}\text{}=\phantom{\rule{0ex}{0ex}}=-\frac{1}{7}\text{}+\frac{5}{49x+35}\phantom{\rule{thinmathspace}{0ex}}.$

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