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Afina-wow [57]
3 years ago
13

Which rational expression is equivalent to 1/(x+4) + 3/(x-5)

Mathematics
1 answer:
Harman [31]3 years ago
6 0

Answer:

(4x+7)/(x^2-x-20)

Step-by-step explanation:

To simplify them into one, you need to make the common denominator (x+4)(x-5).

[1(x-5)+3(x+4)]/(x-5)(x+4)

(x-5+3x+12)/(x-5)(x+4)

(4x+7)/(x-5)(x+4)

I'm not sure how simplified you want it, but as I put at the top, the (x-5)(x+4) can be simplified to x^2-x-20

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Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).
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