Question

For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?

Options

• \[5x-5=\mathrm{A}(x-2)+\mathrm{B}(x-3)\]

• \[5x-5=\mathrm{A}(x-2)(x-3)+\mathrm{B}\]

• \[5x-5=\mathrm{A}(x-3)+\mathrm{B}(x-2)\]

• \[5x-5=\mathrm{A}+\mathrm{B}\]

Answer 1

Multiplying by \[(x-2)(x-3)\] cancels both denominators. The \[\mathrm{A}\]-term retains \[(x-3)\], and the \[\mathrm{B}\]-term retains \[(x-2)\].