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)

2. ...

Originally Posted by soly_sol
Write the partial fraction decomposition of the rational expression.

(x-6)/(x-2)(x-3)
I got: (4)/(x-2) + (3)/(x-3)
the second must be -3

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

....

(4x+2)/(x+3)(x^2+x-3)
I got: (a)/(x+3) + (b)/(x^2+x-3)
it should be bx+c

3. Hello, soly_sol!

Write the form of the partial fraction decomposition of the rational expression.

$\frac{7x+5}{(x-2)(x+5)}$ . . . I got: . $\frac{a}{x-2} + \frac{b}{x+5}$

$\frac{4x-4}{x^2+8x+12}$ . . . I got: . $\frac{a}{x+6} + \frac{b}{x+2}$ . . . . both correct!

Write the partial fraction decomposition of the rational expression.

$\frac{x-6}{(x-2)(x-3)}$ . . . I got: . $\frac{4}{x-2} {\color{red}\,+\,} \frac{3}{x-3}$
. . . . . . . . . . . . . . . . . . . .
minus

$\frac{x}{(x-5)(x-6)}$ . . . I got: . $\frac{-5}{x-5} + \frac{6}{x-6}$

$\frac{x}{x^2-5x+6}$ . . . I got: . $\frac{-2}{x-2} + \frac{3}{x-3}$

$\frac{11x-35}{(x-1)(x-4)}$ . . . I got: . $\frac{8}{x-1}+ \frac{3}{x-4}$

$\frac{12x+52}{(x^2+10x+24}$ . . . I got: . $\frac{2}{x+4} + \frac{10}{x+6}$ . . . . The rest are correct!

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

$\frac{6x-5}{(x+5)^2}$ . . . I got: . $\frac{a}{x+5} + \frac{b}{(x+5)^2}$

$\frac{4x+2}{(x+3)(x^2+x-3)}$ . . . I got: . $\frac{a}{x+3} + \frac{b}{x^2+x-3}$ . . . . no

For a quadratic denominator, we need two terms in the numerator.

. . $\frac{a}{x+3} + \frac{{\color{blue}bx + c}}{x^2+x-3}$