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hjlf
3 years ago
15

Consider Functions F and G

Mathematics
2 answers:
Zanzabum3 years ago
6 0

Answer:

A

Step-by-step explanation:

We are given two functions:

\displaystyle f(x)=\frac{x-16}{x^2+6x-40}\text{ and } g(x)=\frac{1}{x+10}

And we want to find:

f(x)+g(x)

Thus:

\displaystyle =\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}

We can factor the denominator of the first term:

\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}

In order to add the two terms, we must have a common denominator. To achieve this, we can multiply to second term by (x - 4). Therefore:

\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}\Big(\frac{x-4}{x-4}\Big)

Multiply:

\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{x-4}{(x+10)(x-4)}

Combine:

\displaystyle =\frac{(x-16)+(x-4)}{(x+10)(x-4)}

Simplify:

\displaystyle =\frac{2x-20}{(x+10)(x-4)}

We can expand the denominator:

\displaystyle =\frac{2x-20}{x^2+6x-40}

Therefore, our answer is A.

alina1380 [7]3 years ago
3 0

Answer:

A

Step-by-step explanation:

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