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Sever21 [200]
3 years ago
11

Find the partial fraction decomposition of x-3/x(x^2+3)

Mathematics
1 answer:
Setler [38]3 years ago
3 0

Answer:

-1 / x + (x + 1) / (x² + 3)

Step-by-step explanation:

(x − 3) / (x (x² + 3))

There are two factors in the denominator, so split this into two fractions with unknown numerators:

A / x + (Bx + C) / (x² + 3)

Combine back into one fraction:

(A (x² + 3) + (Bx + C) x) / (x (x² + 3))

Now equate this numerator with the original:

A (x² + 3) + (Bx + C) x = x − 3

Ax² + 3A + Bx² + Cx = x − 3

(A + B) x² + Cx + 3A = x − 3

Match the coefficients:

A + B = 0

C = 1

3A = -3

Solve:

A = -1

B = 1

C = 1

Therefore, the partial fraction decomposition is:

-1 / x + (x + 1) / (x² + 3)

Here's a graph showing that the two are the same:

desmos.com/calculator/hrxfnijewh

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5 0
3 years ago
Which is the best estimate of each percent? 25% of 395
NemiM [27]
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3 0
3 years ago
-3 1/2 - 2 1/3 explained
lakkis [162]
The answer is 5 5/6 simplified to the max.

rewrite the equation with separated parts

-3 1/2 - 2 1/3

-3 - 2 = -5

-1/2 - 1/3? u need to find the LEAST common denominator

-3/6 - 2/6 = -5/6

how did I get 6?

Rewriting input as fractions if necessary:
1/2, 1/3

For the denominators (2, 3) the least common multiple (LCM) is 6.

Therefore, the least common denominator (LCD) is 6.

Now lastly combine them total and its -5 - 5/6 = -5 5/6.


5 0
3 years ago
Read 2 more answers
The Sydney cricket ground can contain a football field of approximately 147m by 136m. What distance would be covered by walking
Irina-Kira [14]
The answer is 566m because 147 plus 147 and 136 plus 136 equals 566
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3 years ago
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