Question 1201971
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{{{f = 3/g}}}


{{{3/g = f}}}


{{{g/3 = 1/f}}} Take reciprocal of each side


{{{g/3-1 = 1/f-1}}} Subtract 1 from both sides


{{{g/3-3/3=1/f-f/f}}} Rewrite each "1" as a fraction involving the LCD.


{{{(g-3)/3=(1-f)/f}}}


{{{(g-3)*f=3(1-f)}}} Cross multiply


{{{(g-3)/(1-f) = 3/f}}} Reverse the cross multiplication process, but in a way so the (1-f) goes to the left side.


{{{-(g-3)/(f-1) = 3/f}}}


{{{(g-3)/(f-1) = -3/f}}}


That isn't one of the answer choices, but we could do a bit more algebra
Let's go back to
{{{3/g = f}}}
So
{{{3/g = f}}}
{{{3 = gf}}}
{{{3/f = g}}}


This means
{{{(g-3)/(f-1) = -3/f}}}
turns into
{{{(g-3)/(f-1) = -g}}}


Answer: <font color=red size=4>-g</font> (choice 5)
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