Question

(Х+2)/(х²-2х+1)*(3х-3)/(х²-4)-(3)/(х-2)

Answer 1

Объяснение:

$\frac{x+2}{x^2-2x+1} *\frac{3x-3}{x^2-4} -\frac{3}{x-2} =\frac{x+2}{(x-1)^2}*\frac{3*(x-1)}{(x+2)*(x-2)} -\frac{3}{x-2}=\frac{(x+2)*3*(x-1)}{(x-1)^2*(x+2)*(x-2)}-\frac{3}{x-2} =\\=\frac{3}{(x-1)*(x-2)}-\frac{3}{x-2}=\frac{3}{x-2}*(\frac{1}{x-1}-1)=\frac{3}{x-2}* \frac{1-x+1}{x-1}=\frac{3}{x-2}*\frac{2-x}{x-1}=\\=\frac{3}{x-2}*\frac{x-2}{1-x}=\frac{3*(x-2)}{(x-2)*(1-x)}=\frac{3}{1-x}.$

Answer 2

To simplify the given expression, first factor the denominators and then cancel out any common factors in the fractions. Here's the step-by-step simplification:

Expression: (x + 2) / (x^2 - 2x + 1) * (3x - 3) / (x^2 - 4) - 3 / (x - 2)

Step 1: Factor the denominators:

1. (x^2 - 2x + 1) = (x - 1)^2
2. (x^2 - 4) = (x - 2)(x + 2)

Now, rewrite the expression with the factored denominators:

Expression: (x + 2) / [(x - 1)^2] * (3x - 3) / [(x - 2)(x + 2)] - 3 / (x - 2)

Step 2: Cancel out common factors:

Notice that (x + 2) cancels out in the first and second fractions, and (x - 2) cancels out in the second and third fractions:

Expression: 1 / (x - 1)^2 * 3 - 3 / (x - 2)

Step 3: Combine the fractions:

To combine the fractions, find a common denominator, which is (x - 1)^2 * (x - 2):

Expression: [3 * (x - 2) - 3 * (x - 1)^2] / [(x - 1)^2 * (x - 2)]

Step 4: Distribute and simplify:

Now, distribute and simplify the numerator:

Expression: [3x - 6 - 3(x^2 - 2x + 1)] / [(x - 1)^2 * (x - 2)]

Expression: [3x - 6 - 3x^2 + 6x - 3] / [(x - 1)^2 * (x - 2)]

Combine like terms in the numerator:

Expression: (-3x^2 + 9x - 9) / [(x - 1)^2 * (x - 2)]

So, the simplified expression is (-3x^2 + 9x - 9) / [(x - 1)^2 * (x - 2)].