Answer
$\frac{3}{x-2}+\frac{2}{x-1}$
Work Step by Step
$\frac{5x-7}{x^{2}-3x+2}=\frac{5x-7}{(x-2)(x-1)}$
Decomposing to partial fractions, we have
$\frac{5x-7}{(x-2)(x-1)}=\frac{A}{x-2}+\frac{B}{x-1}$
This gives $5x-7= A(x-1)+B(x-2)$.
Equating the coefficients of x and the constant term, we obtain
A+B=5 and A+2B=7.
Solving these equations, we get A=3 and B=2.
Thus $\frac{5x-7}{x^{2}-3x+2}=\frac{3}{x-2}+\frac{2}{x-1}$
