What is the restrictions for the following rational expression?

Question

-2x/3 = -3x/5 - 2/3: This is the equation and I am trying to determine what are the restrictions or if there any restrictions of this rational expressions.

Answer 1

To solve this problem, you need to get your variables all on one side with everything else on the other side. Therefore, starting out with:

-2x/3 = -3x/5 - 2/3, move the "-3x/5" to the other side of the equation, like so:

-2x/3 + 3x/5 = -3x/5 + 3x/5 - 2/3 (whatever you do to one side of the equation, you have to do to the other). This gives you:

-2x/3 + 3x/5 = - 2/3. Next, find the lowest common denominator for both fractions by finding the least common multiple of each denominator. The first few multiples of 3 are 3, 6, 9, 12, and 15. The first few multiples of 5 are 5, 10, and 15. Both have 15 in common. So

-2x/3 = ?/15 and 3x/5 = ?/15. 3 x 5 is 15, so multiply the first fraction by 5/5 and the second by 3/3 (whatever you do to the denominator, you must do to the numerator). This gives you:

-2x/3 x 5/5 = -10x/15, and 3x/5 x 3/3 = 9x/15. Now, plug -10x/15 and 9x/15 back into your original equation:

-2x/3 + 3x/5 = -2/3 is now

-10x/15 + 9x/15 = -2/3. Add the fractions and you get:

-x/15 = -2/3. Now, you have to multiply both sides by 15 to get rid of the denominator:

-x/15 x 15 = -2/3 x 15 = (-2 x 15)/3

-x = -30/3

-x = -10, therefore, x = 10.

To check, substitute 10 for X in your original equation and you get.

(-2 x 10)/3 = (-3 x 10)/5 - 2/3

-20/3 = -30/5 -2/3

-20/3 + 2/3 = -30/5 - 2/3 + 2/3

-18/3 = -30/5 . -18 divided by 3 = -6 and -30 divided by 5 = -6, so -6 = -6. Therefore, x = 10 is the correct answer.