Precalculus (6th Edition) Blitzer

The simplified partial fraction expansion is $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}=\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$
The provided rational expression is as follows: $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}$ Now, solving the expression as given below: 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. Then, decompose the fractional part as follows: $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}=\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$ Thus, $\frac{A}{\left( x-1 \right)}+\frac{B}{\left( x+3 \right)}$ is a partial fraction expansion of the rational expression $\frac{5x+7}{\left( x-1 \right)\left( x+3 \right)}$ with constants $A$ and $B$.