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Ivan
3 years ago
7

Write the partial fraction decomposition fro the ration expression below

Mathematics
1 answer:
zlopas [31]3 years ago
6 0
\dfrac{5x-2}{(x-1)^2}=\dfrac a{x-1}+\dfrac b{(x-1)^2}
5x-2=a(x-1)+b

Since 5x-2=5x-5+3=5(x-1)+3, it follows that a=5 and b=3, so

\dfrac{5x-2}{(x-1)^2}=\dfrac5{x-1}+\dfrac3{(x-1)^2}

\dfrac{x^3+x^2+x+2}{x^4+x^2}=\dfrac{x^3+x+x+2}{x^2(x^2+1)}=\dfrac ax+\dfrac b{x^2}+\dfrac{cx+d}{x^2+1}
x^3+x^2+x+2=ax(x^2+1)+b(x^2+1)+(cx+d)x^2
x^3+x^2+x+2=(a+c)x^3+(b+d)x^2+ax+b

When x=0, you find that b=2. It's also clear that a=1. So the remaining constants must be 1+c=1\implies c=0 and 2+d=1\implies d=-1, and so you get

\dfrac{x^3+x^2+x+2}{x^4+x^2}=\dfrac1x+\dfrac2{x^2}-\dfrac1{x^2+1}
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The sum of 3 consecutive integers is 47 more than the first integer. Find the three integers.
ss7ja [257]

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Step-by-step explanation:

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What is 8-8 to the power of -1 ?
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3 years ago
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