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olga nikolaevna [1]
3 years ago
6

(1 ÷ x- 1)+(2÷ x+2)=(3÷2) solve and check for extraneous solutions

Mathematics
1 answer:
Sliva [168]3 years ago
5 0
\frac{1}{x-1}+ \frac{2}{x+2}= \frac{3}{2}
\frac{1(x+2)}{(x-1)(x+2)}+ \frac{2(x-1)}{(x+2)(x-1)}= \frac{3(x-1)(x+2)}{2}
\frac{x+2+2(x-1)}{(x-1)(x+2)}= \frac{3(x-1)(x+2)}{2}
\frac{x+2+2x-1}{(x-1)(x+2)}= \frac{3(x-1)(x+2)}{2}
\frac{3x+1}{(x-1)(x+2)}= \frac{3(x^2+x-2)}{2}
\frac{}{(x-1)(x+2)}= \frac{3x^2+3x-6)}{2}
\frac{3x+1}{(x^2+x-2)}= \frac{3x^2+3x-6)}{2}
\frac{2(3x+1)}{2(x^2+x-2)}= \frac{3x^2+3x-6)(x^2+x-2)}{2(x^2+x-2)}
\frac{2(3x+1)}{2(x^2+x-2)}-\frac{3x^2+3x-6)(x^2+x-2)}{2(x^2+x-2)}=0
\frac{2(3x+1)-3x^2+3x-6}{2(x^2+x-2)}=0

this will be continued
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The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
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We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

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Then, if we apply the natural logarithm we get:

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