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Sphinxa [80]
3 years ago
7

Which expression is equal to f(x) + g(x)?

Mathematics
1 answer:
eimsori [14]3 years ago
7 0

Answer:

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

Step-by-step explanation:

f(x)+g(x)

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

I'm going to factor that quadratic in the first fraction's denominator to figure out what I need to multiply top and bottom of the other fraction or this fraction so that I have a common denominator.

I want a common denominator so I can write as a single fraction.

So since the leading coefficient is 1, all we have to do is find two numbers that multiply to be c and at the same thing add up to be b.

c=-40

b=6

We need to find two numbers that multiply to be -40 and add to be 6.

These numbers are 10 and -4 since (10)(-4)=-40 and 10+-4=6.

So the factored form of x^2+6x-40 is (x+10)(x-4).

So the way the bottoms will be the same is if I multiply top and bottom of my second fraction by (x-4).

This will give me the following sum so far:

\frac{x-16}{x^2+6x-40}+\frac{x-4}{x^2+6x-40}

Now that the bottoms are the same we just need to add the tops and then we are truly done:

\frac{(x-16)+(x-4)}{x^2+6x-40}

\frac{x+x-16-4}{x^2+6x-40}

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

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