College Algebra Question?

Question

Solve the following equation by the method of your choice-

2/(3x-1) = 3/(x+1)

THANKS!!!

Answer 1

Step 1:Rewrite the equation
2 / ( 3x - 1) = 3 / ( x + 1)

Step 2:Cross-multiply
2(x + 1) = 3(3x - 1)

Step 3:Expand the equation
2x + 2 = 9x - 3

Step 4:Place the unknowns on the LHS & values on the RHS
2x - 9x = -3 - 2

Step 5:Solve simple subtraction on both sides.
-7x = -5

Step 6:Final answer
x = 5/7

Answer 2

First:

multiply by a common denominator.
2/(3x-1) must be multiplied by (x+1)
and
3/(x+1) must be multiplied by (3x-1)

So: (2(x+1))/((3x-1)(x+1)) = (3(3x-1))/((3x-1)(x+1))

Distribute

(2x+2) / (3x^2+2x-1) = (9x-3) / (3x^2 +2x -1)

Subtract

[(2x+2) - (9x-3)] / (3x^2 + 2x -1) = 0
=(5 - 7x) / (3x^2 +2x -1) = 0

Solve for the top, because when the top part of a fraction equals 0, the entire thing does. When the bottom equals 0, it fails to exist.

So:
5 - 7x = 0
add the 7 to the other side
divide by 7

5 = 7x
x= 5/7

Answer 3

Multiply each side by (3x-1)
2= 3(3x-1)/(x+1)
Multiply each side by (x+1)
2(x+1)= 3(3x-1)
Expand each side
2x+2= 9x-3
Subtract 2x from each side
2= 7x-3
add 3 to each side
5= 7x
Divide both sides by 7
5/7 = x
Go home and have a beer.

Answer 4

My method, easiest I think, is cross-multiply.

3(3x - 1) = 2(x + 1)
9x - 3 = 2x + 2
7x = 5
x = 5/7

Answer 5

2/(3x - 1) = 3/(x + 1)

Cross multiply;

2(x + 1) = 3(3x - 1)

Distribute

2x + 2 = 9x - 3

Isolate x.

5 = 7x
5/7 = x

Answer 6

a/b = c/d implies that ad = bc
So.... 2(x+1) = 3(3x-1)
2x+2 = 9x-3
2x+5 = 9x
5 = 7x
5/7 = x

Answer 7

Cross mult to get 2x+2 = 9x-3
Collect terms to get 5= 7x or x= 5/7

Answer 8

No, that would be high school algebra.