Please check my answers.

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.

(7x+5)/(x-2)(x+5)

I got: (a)/(x-2) + (b)/(x+5)

(4x-4)/(x^2+8x+12)

I got: (a)/(x+6) + (b)/(x+2)

Write the partial fraction decomposition of the rational expression.

(x-6)/(x-2)(x-3)

I got: (4)/(x-2) + (3)/(x-3)

(x)/(x-5)(x-6)

I got: (-5)/(x-5) + (6)/(x-6)

(x)/(x^2-5x+6)

I got: (-2)/(x-2) + (3)/(x-3)

(11x-35)/(x-1)(x-4)

I got: (8)/(x-1)+ (3)/(x-4)

(12x+52)/(x^2+10x+24)

I got: (2)/(x+4) + (10)/(x+6)

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.

(6x-5)/(x+5)^2

I got: (a)/(x+5) + (b)/(x+5)^2

(4x+2)/(x+3)(x^2+x-3)

I got: (a)/(x+3) + (b)/(x^2+x-3)