Partial fraction decomposition for the rational function : .

First factor the denominator  .

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Now, the rational function is .

Include one partial fraction for each factor.

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Where, A, B, and C are to be determined.Multiplying this equation by least common denominator x(x + 7)(x - 5) yields the basic equation.

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To solve for A, let, - 35A = 2

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To solve for B and C, let,

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Put,  in the above equations.

Solve eq (1) & (2) For, B and C.

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Substitute the value in eq (1).

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Therefore, .