Partial fraction decomposition. Write the ratio (3x+2)/(x^2+x) using partial fraction decomposition.

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The partial fractions of (3x+2)/(x^2+x) have to be determined.

(3x+2)/(x^2+x)

=> (3x+2)/x(x + 1)

This can be written as A/x + B/(x + 1)

A/x + B/(x + 1) = (3x+2)/[x(x + 1)]

Ax + A + Bx = 3x + 2

=> A + B = 3 and A...

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The partial fractions of (3x+2)/(x^2+x) have to be determined.

(3x+2)/(x^2+x)

=> (3x+2)/x(x + 1)

This can be written as A/x + B/(x + 1)

A/x + B/(x + 1) = (3x+2)/[x(x + 1)]

Ax + A + Bx = 3x + 2

=> A + B = 3 and A = 2

=> B = 1

The partial fractions are 2/x + 1/(x + 1)

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