Answer
The statement makes sense.
Work Step by Step
Let us consider an example as follows:
$\frac{3}{x}+\frac{1}{x+2}$
Firstly, check the common denominator of the fraction.
$x\left( x+2 \right)$
Next to operate the partial fraction decomposition:
$\frac{3\left( x+2 \right)+1}{x\left( x+2 \right)}=\frac{3x+7}{x\left( x+2 \right)}$
Writing the fraction with one of the polynomial factors for each of the denominator.
$\frac{3x+7}{x\left( x+2 \right)}=\frac{A}{x}+\frac{B}{x+2}$
And by multiplying both sides by the common factors $x\left( x+2 \right)$.
$\begin{align}
& 3x+7=A\left( x+2 \right)+Bx \\
& 3x+7=Ax+2A+Bx \\
& 3x+7=\left( A+B \right)x+2A \\
\end{align}$
And equating the equation:
$\begin{align}
& A+B=3 \\
& 2A=7 \\
\end{align}$
Then, solving the above equation for $A$ and $B$.
$A=\frac{7}{2},B=-\frac{1}{2}$
Put these values in $\frac{3x+7}{x\left( x+2 \right)}=\frac{A}{x}+\frac{B}{x+2}$
$\frac{3x+7}{x\left( x+2 \right)}=\frac{7}{2x}-\frac{1}{2\left( x+2 \right)}$.
Thus, the statement makes sense.
