simplify
(x+2)/(x) divided by (x-2)/(3x)
(x+2)/(x) divided by (x-2)/3x =
invert the denominator and multiply.
(x+2)/(x) times (3x)/(x-2)
cancel like terms.
To simplify the expression (x+2)/(x) divided by (x-2)/(3x), we can follow these steps:
Step 1: Invert the denominator and multiply.
Take the reciprocal of the second fraction, which is (x-2)/(3x), to get (3x)/(x-2). Now, our expression becomes (x+2)/(x) times (3x)/(x-2).
Step 2: Multiply the numerators and multiply the denominators.
Multiply the numerators (x+2) and (3x) together to get (x+2)(3x) = 3x^2 + 6x.
Multiply the denominators (x) and (x-2) together to get (x)(x-2) = x^2 - 2x.
Step 3: Simplify or cancel like terms.
Since there are no like terms that can be canceled, we leave the expression as it is:
(3x^2 + 6x)/(x^2 - 2x)
Therefore, the simplified form of (x+2)/(x) divided by (x-2)/(3x) is (3x^2 + 6x)/(x^2 - 2x).