Question

What are the values of \[\mathrm{A}\] and \[\mathrm{B}\] in \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\]?

Options

• \[\mathrm{A}=10,\ \mathrm{B}=-5\]

• \[\mathrm{A}=5,\ \mathrm{B}=10\]

• \[\mathrm{A}=-5,\ \mathrm{B}=10\]

• \[\mathrm{A}=5,\ \mathrm{B}=-10\]

Answer 1

From \[\mathrm{A}+\mathrm{B}=5\], use \[\mathrm{B}=5-\mathrm{A}\]. Substitution into \[3\mathrm{A}+2\mathrm{B}=5\] gives \[\mathrm{A}=-5\] and \[\mathrm{B}=10\].