First simplify the expression 6x: (x²-y²) -3: (x-y) then substitute at x = (- 2/3) y = 3/4.

| July 26, 2021 | education

Let’s open the brackets, applying the formula of abbreviated multiplication a ^ 2 – b ^ 2 = (a + b) * (a – b), we get:

6 * x / ((x + y) * (x – y)) – 3 / (x – y).

Find a common denominator – (x + y) * (x – y).

The factor of the numerator of the first expression is ((x + y) * (x – y)) / ((x + y) * (x – y)) = 1.

The factor of the numerator of the second expression is ((x + y) * (x – y)) / (x – y) = (x + y).

Means:

6 * x / ((x + y) * (x – y)) – 3 / (x – y) = ((6 * x * 1) – (3 * (x + y)) / ((x + y ) * (x – y)) = (6 * x – 3 * x – 3 * y) / ((x + y) * (x – y)) = (3 * x – 3 * y) / ((x + y) * (x – y)) = (3 * (x – y)) / ((x + y) * (x – y)) = 3 / (x + y).

Let’s substitute in the found expression the values ​​of the variables x = -2/3 and y = 3/4.

3 / (x + y) = 3 / (-2/3 + 3/4) = 3 / ((-2 * 4 + 3 * 3) / 12) = 3 / ((-8 + 9) / 12) = 3 / 1/12 = 3 * 12 = 36.

Answer: the value of the expression 6 * x / (x2 – y2) – 3 / (x – y) at x = -2/3 and y = 3/4 takes the value 36.



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