Solving Rational Equations! HELP!!! Please?

Question

2/x - 3/2x = 1/3

Solve for x.

Please show how you got the answer. I know it comes to x = 3/2 but I can't figure out how it gets to that answer.

Please explain using the LCD method.

I understand how the other one works but my teacher won't accept the answer if it's not using the LCD method.

HELP PLEASE!

Thank you in Advance!

Answer 1

First, please respect the order of operations -- multiplication and division have the same precedence, so when you write 3/2x, it means (3/2)x and not what you intend it to mean, namely 3/(2x). If you want the division operator to apply to a product of two numbers, you have to put them in parentheses.

Anyway, first you would add the fractions just like you would add any other fraction, namely by finding a common denominator. This means you must find a common multiple of x and 2x -- obviously, 2x suffices. Therefore, multiply the numerator and denominator of the first fraction to obtain:

4/(2x) - 3/(2x) = 1/3

Now add the fractions:

1/(2x) = 1/3

Multiply by 3x:

3/2 = x

And we are done.