Question

For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?

Options

• \[A=1,\quad B=\frac12\]

• \[A=\frac12,\quad B=\frac14\]

• \[A=\frac14,\quad B=2\]

• \[A=\frac14,\quad B=\frac12\]

Answer 1

Equating coefficients of \[x\] gives \[4A=1\], so \[A=\frac14\]. Equating constant terms gives \[6A+B=2\], which yields \[B=\frac12\].