3x-27/55÷x-9/15x my answer is =3(11x^2-4)/11x

is this correct.

It depends upon where you put the parentheses in the question.

there is no parentheses in the math problem

But when you type out the expression on a single line, you need paretheses to define the order of operation.

There are many ways a person could interpret what you have typed, and all give different answers.

Two possibilites would be
3x - (27/25) /[(x-9)/15x]
and
[(3x-27)/55] / [x-(9/15x)]

To check if your answer is correct, we can simplify the expression step by step.

Given expression: 3x - 27/55 ÷ x - 9/15x

Step 1: Simplify the division
To simplify the expression, we need to find the reciprocal of the second fraction and multiply it with the first fraction.

3x - 27/55 ÷ x - 9/15x
= 3x - 27/55 * 1/x - 9/15x

Multiplying fractions:
= 3x - 27/55 * 1/x - 9/(15 * x)
= 3x - 27/55x - 9/15x

Step 2: Find the common denominator
To combine the two fractions, we need to find the least common denominator (LCD). The LCD for 55x and 15x is 165x.

= (3x * 165x - 27 * 3x - 9 * 11x) / [55x * 165x]
= (495x^2 - 81x - 99x) / 9075x^2
= (495x^2 - 180x) / 9075x^2
= 15x(33x - 12) / 225(x^2)
= 5x(11x - 4)/ 75(x^2)

So the simplified expression is 5x(11x - 4)/75(x^2).

Your answer, 3(11x^2 - 4)/11x, is not correct. The correct simplified expression is 5x(11x - 4)/75(x^2).