$f (x) = 3 x - 1$ $f(x)=3x-1$ and $g (x) = x - 2$ $g(x)=x-2$ . How do you solve $(\frac{f}{g}) (x)$ $(f/g)(x)$ ?

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Answer 1 · 2017-10-23T01:11:31

$x = \frac{1}{3}$ $x=1/3$

Refer to the explanation for the process.

$f (x) = 3 x - 1$ $f(x)=3x-1$

$g (x) = x - 2$ $g(x)=x-2$

$(\frac{f}{g}) (x)$ $(f/g)(x)$ means to divide the expression for $f (x)$ $f(x)$ by the expression for $g (x)$ $g(x)$ .

$(\frac{f}{g}) (x) = \frac{3 x - 1}{x - 2}$ $(f/g)(x)=(3x-1)/(x-2)$

Set $(\frac{f}{g}) (x)$ $(f/g)(x)$ equal to $0$ $0$ .

$0 = \frac{3 x - 1}{x - 2}$ $0=(3x-1)/(x-2)$

Multiply both sides by $(x - 2)$ $(x-2)$ .

$0(x-2)=(3x-1)/color(red)cancel(color(black)((x-2)))^1xxcolor(red)cancel(color(black)((x-2)))^1$

Simplify.

$0=3x-1$

Switch sides.

$3x-1=0$

Add $1$ to both sides.

$3x=1$

Divide both sides by $3$ .

$x=1/3$

f(x)=3x-1f(x)=3x−1f(x)=3x-1 and g(x)=x-2g(x)=x−2g(x)=x-2. How do you solve (f/g)(x)(fg)(x)(f/g)(x)?