Question

Which decomposition is correct for \[\frac{x^{2}+1}{x^{2}-5x+6}\]?

Options

• \[\frac{5}{x-2}+\frac{10}{x-3}\]

• \[1+\frac{5}{x-2}-\frac{10}{x-3}\]

• \[1-\frac{5}{x-2}-\frac{10}{x-3}\]

• \[1-\frac{5}{x-2}+\frac{10}{x-3}\]

Answer 1

Long division produces the quotient \[1\], and partial fractions give \[\mathrm{A}=-5\], \[\mathrm{B}=10\]. Combining these results gives the stated decomposition.