Ения: (a ^ 2 + ax)/x / ((ax)/(x ^ 2)) 7a + (2a - 7e ^ 2)/6 12/(2a - a ^ 1) - 6/a (xy + y ^ 2)/(15x) * (3x)/(x + y) 6/(x + 3) - x/((x + 3) ^ 2) / (x/(x ^ 2 - 9)) - (2x + 18)/(x + 3)

To simplify these expressions, we'll follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction. Let's solve them step by step:

Expression 1: (a^2 + ax)/x / ((ax)/(x^2))

To simplify this expression, we need to divide the numerator by the denominator: (a^2 + ax)/x * (x^2/(ax))

Next, we can cancel out common factors: (a^2 + ax) * (x^2/(ax))

Now we can multiply across: (a^2x^2 + ax^3)/(ax)

Expression 2: 7a + (2a - 7e^2)/6

There's nothing to simplify here. This is already in its simplest form.

Expression 3: 12/(2a - a^1) - 6/a

To simplify this expression, we'll simplify the denominators first: 12/(2a - a) - 6/a

Simplifying the denominators further: 12/(a) - 6/a

Now we can find a common denominator: (12 - 6)/a

Simplifying further: 6/a

Expression 4: (xy + y^2)/(15x) * (3x)/(x + y)

To simplify this expression, we can cancel out common factors: (y(x + y))/(15x) * (3x)/(x + y)

Now we can multiply across: (3xy(x + y))/(15x(x + y))

We can cancel out common factors again: 3y/(15x)

Finally, we can simplify the fraction: y/(5x)

Expression 5: 6/(x + 3) - x/((x + 3)^2) / (x/(x^2 - 9)) - (2x + 18)/(x + 3)

To simplify this expression, let's work through the calculations step by step: 6/(x + 3) - x/((x + 3)^2) - (2x + 18)/(x + 3)

Now, we need to find a common denominator: (6(x^2 - 9))/(x + 3) - x/((x + 3)^2) - (2x + 18)/(x + 3)

Combine the fractions: (6(x^2 - 9) - x(x + 3) - (2x + 18))/(x + 3)

Expand and simplify: (6x^2 - 54 - x^2 - 3x - 2x - 18)/(x + 3)

Combine like terms: (5x^2 - 5x - 72)/(x + 3)

This is the final simplified form of the expression.