Answer
The simplified partial fraction expansion is $\frac{11x-10}{\left( x-2 \right)\left( x+1 \right)}=\frac{A}{\left( x-2 \right)}+\frac{B}{\left( x+1 \right)}$.
Work Step by Step
The provided rational expression is as follows:
$\frac{11x-10}{\left( x-2 \right)\left( x+1 \right)}$
Now, solving the expression as follows:
We set up the partial fraction expansion with unknown constants coefficients and then write a constant coefficients over each of the two distinct algebraic linear factors in the denominator of the expression.
Now, decomposing the fractional part as follows:
$\frac{11x-10}{\left( x-2 \right)\left( x+1 \right)}=\frac{A}{\left( x-2 \right)}+\frac{B}{\left( x+1 \right)}$
Thus, $\frac{A}{\left( x-2 \right)}+\frac{B}{\left( x+1 \right)}$ is a partial fraction expansion of rational expression $\frac{11x-10}{\left( x-2 \right)\left( x+1 \right)}$ with constants $A$ and $B$.
