Question

Make m the subject of the formula f=4m+3/m-1

Answer 1

Answer:

$\boxed{\sf m = \frac{ - (f + 3)}{4 - f}}$

Step-by-step explanation:

$\sf Solve \: for \: m: \\ \sf \implies f = \frac{4m + 3}{m - 1} \\ \\ \sf \: f = \frac{4m + 3}{m - 1} \: is \: equivalent \: to \: \frac{4m + 3}{m - 1} = f : \\ \sf \implies \frac{4m + 3}{m - 1} = f \\ \\ \sf Multiply \: both \: sides \: by \: m - 1: \\ \sf \implies \frac{4m + 3}{ \cancel{m - 1}} \times \cancel{m - 1} = f(m - 1) \\ \\ \sf \implies 4m + 3 = f(m - 1) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies 4m + 3 = fm - f \\ \\ \sf Subtract \: (f m + 3) \: from \: both \: sides: \\ \sf \implies 4m + 3 - (fm + 3) = fm - f - (fm + 3) \\ \\ \sf \implies 4m + 3 - fm - 3 = fm - f - fm - 3 \\ \\ \sf \implies 4m - fm + 3 - 3 = fm - fm - f - 3 \\ \\ \sf \implies 4m - fm = - f - 3 \\ \\ \sf \implies m(4 - f) = - (f + 3) \\ \\ \sf Divide \: both \: sides \: by \: (4 - f): \\ \sf \implies \frac{m \cancel{(4 - f)}}{\cancel{(4 - f)}} = \frac{ - (f + 3)}{4 - f} \\ \\ \sf \implies m = \frac{ - (f + 3)}{4 - f}$