### MODERATE EXERCISES - Partial Fractional Decompositions

**(1)** Find the constants A and B so that the given
equation is true on its domain.

3x^{2}+ 7x + 1 A B C ------------ = - + ----- - -------- x(x + 1)^{2}x x + 1 (x + 1)^{2}

**(2)** Decompose the following fraction into
partial fractions.

8x - 3 ------- 2x^{2}- x

**(3)** Find the constants A and B so that the
given equation is true on its domain.

5x^{2}- 9x + 19 A Bx + C --------------- = ----- + -------- (x - 4)(x^{2}+ 5) x - 4 x^{2}+ 5

**(4)** Decompose the following fraction into
partial fractions.

3x - 13 ------------ 6x^{2}- x - 12