List of top Mathematics Questions on Partial Fractions

If $\frac{42-19x}{(x^{2}+1)(x-4)}=\frac{Ax+B}{x^{2}+1}+\frac{C}{x-4}$ then $B =$

If \[ \frac{f(x)}{(x-1)(x-2)} = \frac{2}{x-2} - \frac{1}{x-1} \] and \[ f(x)+\frac{xf(x)}{(x-1)(x-2)} = g(x)+\frac{A}{x-2}+\frac{B}{x-1}, \] then $g(A+B)=$

If \[ \frac{3x^2+x+2} {(3x^2+x+4)(3x^2+x+1)} = \frac{Ax+B}{3x^2+x+4} + \frac{Cx+D}{3x^2+x+1}, \] then \((A+B)+(C+D)\) is:

The partial fraction decomposition of \( \frac{x^{4}+24 x^{2}+28}{(x^{2}+1)^{3}} \) is

If \[ \frac{x}{(x^2+1)^2(x-1)} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x-1}, \] then \[ A+B-C+2D= \]

If $\frac{3x + 4}{(x-1)(x-2)^2} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}$, then $A + B + C =$

If \(\frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3}\), then the values of (A, B, C) are

If \(\frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1} + \frac{B}{x+3}\), then A+B =

If $\frac{3x}{x^2+x-2} = \frac{A}{x+2} + \frac{B}{x-1}$, then the ordered pair $(A, B)$ is

If $\deg f(x) \geq \deg g(x)$, then the rational fraction $\frac{f(x)}{g(x)}$ is called

If $\deg f(x) \geq \deg g(x)$, then the rational fraction $\frac{f(x)}{g(x)}$ is called

If $\frac{3x}{x^2+x-2} = \frac{A}{x+2} + \frac{B}{x-1}$, then the ordered pair $(A, B)$ is

The expression \[ \frac{x^4}{(x^2+1)(x^2+3)} \] is equal to

If \[ \frac{4x^3+16x+7}{(x^2+4)^2} = \frac{Ax+B}{x^2+4} + \frac{Cx+D}{(x^2+4)^2}, \] then the number of non-zero values in \(A,B,C,D\) is

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is given by \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(C\) is

Evaluate \[ \lim_{n\to \infty}\sum_{r=1}^{n}\frac{r+2}{r(r+1)(r+3)} \] is equal to:

If we resolve the rational fraction \[ \frac{1}{(1-2x)^2(1-3x)} \] into partial fractions of the form \[ \frac{A}{1-3x}+\frac{B}{1-2x}+\frac{C}{(1-2x)^2}, \] then what is the \(\min\{A,B,C\}=\)

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is of the form \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(A+B+C\) is:

If \[ \frac{2x^2+1}{x^3-1} = \frac{A}{x-1} + \frac{Bx+C}{x^2+x+1}, \] then \[ 7A+2B+C= \]

If \[ \frac{13x+43}{2x^2+17x+30} = \frac{A}{2x+5} + \frac{B}{x+6}, \] then \(A^2+B^2=\)