Respuesta :

Cathenna

Answer:

[tex] \boxed{\sf m = \frac{ - (f + 3)}{4 - f}} [/tex]

Step-by-step explanation:

[tex] \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} [/tex]

abidemiokin

The value of m as a function of "f" is [tex]m =\frac{3+f}{f-4}\[/tex]

Given the expression f=4m+3/m-1, we are to write m as a function of "f"

Rewrite the expression to have:

[tex]f=\frac{4m+3}{m-1}[/tex]

Cross multiply

[tex]f(m-1)=4m+3\\fm - f = 4m + 3\\fm-4m=3+f\\m(f-4)=3+f[/tex]

Divide both sides by f- 4 to have;

[tex]\frac{m(f-4)}{f-4} =\frac{3+f}{f-4}\\m =\frac{3+f}{f-4}\\[/tex]

Hence the value of m as a function of "f" is [tex]m =\frac{3+f}{f-4}\[/tex]

Learn more on subject of formula here:https://brainly.com/question/21406377