(a-2b) : (1/2a-b)

To simplify the expression (a-2b) : (1/2a-b), we can follow these steps:

Step 1: Multiply both the numerator and the denominator by the reciprocal (or the inverse) of the divisor.

In this case, the divisor is (1/2a-b). To find its reciprocal, we flip it, which gives us the fraction (2a-b)/1.

Now, the expression becomes:

(a-2b) * (2a-b) / 1

Step 2: Multiply the numerators together and multiply the denominators together.

(a-2b) * (2a-b) = (a * 2a) + (a * -b) + (-2b * 2a) + (-2b * -b)

Simplifying this, we have:

2a^2 - ab - 4ab + 2b^2

Step 3: Cancel out like terms if possible.

In this case, we can combine the -ab and -4ab terms:

2a^2 - 5ab + 2b^2

So, the simplified expression is 2a^2 - 5ab + 2b^2.