Is x/2-x/3= 6 a rational expression? show work

Yes, this is a rational expression.

A rational expression is any number that can be expressed as a fraction or ratio with two numbers.

Example: 2/3, x/3, 5/3, 3/x.

In this case, we're given x/2 - x/3 = 6

Let's solve this equation.

All denominators must be equal to solve this, so we're going to multiply both halves of the first fraction by 3, and both halves of the 2nd by 2.

3x/6 - 2x/6 = 6

Now, we can multiply all terms by 6 to cancel the first two denominators.

3x - 2x = 36

Now, combine like terms and solve:

x = 36

If we plug in this value of x into the original equation, it will be equal.

36/2 - 36/3 = 6

18 - 12 = 6

6 = 6

36 can be expressed as 36/1, or just 36, which means it is rational.

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step-by-step explanation: