SOLUTION: if f=3/g, where g is not equal to 0 and f is not equal to 1, which of the following is equal to g-3/f-1 1)g 2)f 3)g-f 4)-f 5)-g

Algebra ->  Equations -> SOLUTION: if f=3/g, where g is not equal to 0 and f is not equal to 1, which of the following is equal to g-3/f-1 1)g 2)f 3)g-f 4)-f 5)-g      Log On


   

Question 1201971: if f=3/g, where g is not equal to 0 and f is not equal to 1, which of the following is equal to g-3/f-1
1)g
2)f
3)g-f
4)-f
5)-g
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

f+=+3%2Fg

3%2Fg+=+f

g%2F3+=+1%2Ff Take reciprocal of each side

g%2F3-1+=+1%2Ff-1 Subtract 1 from both sides

g%2F3-3%2F3=1%2Ff-f%2Ff Rewrite each "1" as a fraction involving the LCD.

%28g-3%29%2F3=%281-f%29%2Ff

%28g-3%29%2Af=3%281-f%29 Cross multiply

%28g-3%29%2F%281-f%29+=+3%2Ff Reverse the cross multiplication process, but in a way so the (1-f) goes to the left side.

-%28g-3%29%2F%28f-1%29+=+3%2Ff

%28g-3%29%2F%28f-1%29+=+-3%2Ff

That isn't one of the answer choices, but we could do a bit more algebra
Let's go back to
3%2Fg+=+f
So
3%2Fg+=+f
3+=+gf
3%2Ff+=+g

This means
%28g-3%29%2F%28f-1%29+=+-3%2Ff
turns into
%28g-3%29%2F%28f-1%29+=+-g

Answer: -g (choice 5)

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You have not shown the expression correctly, so none of the given answer choices is correct.

g-3/f-1 --> g-3%2Ff-1

Substitute 3/g for f:

g-3%2F%283%2Fg%29-1
g-3%28g%2F3%29-1
g-g-1
-1

ANSWER: -1

You can get yourself into all kinds of trouble if you are sloppy with your use of parentheses.

From the given answer choices, it is clear that the expression to be simplified is in fact

(g-3)/(f-1) --> %28g-3%29%2F%28f-1%29

Let's do that....

Substitute 3/g for f and simplify:

%28g-3%29%2F%283%2Fg-1%29
%28g-3%29%2F%28%283-g%29%2Fg%29
%28g-3%29%2A%28g%2F%283-g%29%29
-g

ANSWER: -g (answer choice 5)

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
system%28f=3%2Fg%2Cand%2Cg-3%2Ff-1%29

also, g=3%2Ff.

(1)
g-3%2F%283%2Fg%29-1
g-3%28g%2F3%29-1
g-g-1
-1

(2)
%283%2Ff%29-3%2Ff-1
3%2Ff-3%2Ff-1
0-1
-1