Y=(√x^2-8x+12)/3+(2x^2)/(x-3)-5/(x+1)

Question 1

Задача Задача №34595

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Аноним

06 ноября 2023 14:37 · публичный вопрос

А

Аноним 06 ноября 2023 14:37

Y=(√x^2-8x+12)/3+(2x^2)/(x-3)-5/(x+1)

Answer

To simplify the expression, let's break it down step by step.

Start by simplifying the numerator of the first term, √x^2 - 8x + 12. This can be further simplified by factoring the expression inside the square root: √x^2 - 8x + 12 = √(x - 2)(x - 6).
Rewrite the expression with the simplified numerator: y = (√(x - 2)(x - 6))/3 + (2x^2)/(x - 3) - 5/(x + 1).
Simplify the second term, (2x^2)/(x - 3). To do this, we can divide 2x^2 by (x - 3): (2x^2)/(x - 3) = (2x)(x)/(x - 3) = 2x.
Now, rewrite the expression with the simplified second term: y = (√(x - 2)(x - 6))/3 + 2x - 5/(x + 1).
Finally, we need to simplify the third term, 5/(x + 1). This can be simplified by multiplying both the numerator and denominator by (x - 1): 5/(x + 1) = 5(x - 1)/(x + 1)(x - 1) = 5(x - 1)/(x^2 - 1).
The expression can now be further simplified: y = (√(x - 2)(x - 6))/3 + 2x - 5(x - 1)/(x^2 - 1).

That's the simplified expression!

Question 2

y=(√x^2-8x+12)/3+(2x^2)/(x-3)-5/(x+1)

Answer

To simplify the expression, let's break it down step by step. 1. Start by simplifying the numerator of the first term, √x^2 - 8x + 12. This can be further simplified by factoring the expression inside the square root: √x^2 - 8x + 12 = √(x - 2)(x - 6). 2. Rewrite the expression with the simplified numerator: y = (√(x - 2)(x - 6))/3 + (2x^2)/(x - 3) - 5/(x + 1). 3. Simplify the second term, (2x^2)/(x - 3). To do this, we can divide 2x^2 by (x - 3): (2x^2)/(x - 3) = (2x)(x)/(x - 3) = 2x. 4. Now, rewrite the expression with the simplified second term: y = (√(x - 2)(x - 6))/3 + 2x - 5/(x + 1). 5. Finally, we need to simplify the third term, 5/(x + 1). This can be simplified by multiplying both the numerator and denominator by (x - 1): 5/(x + 1) = 5(x - 1)/(x + 1)(x - 1) = 5(x - 1)/(x^2 - 1). 6. The expression can now be further simplified: y = (√(x - 2)(x - 6))/3 + 2x - 5(x - 1)/(x^2 - 1). That's the simplified expression!