Question

(3x-8x²):(x-1)²+(2x²+3x³):(1-x)²

Answer 1

Ответ:

(3x-8x²):(x-1)²+(2x²+3x³):(1-x)²

(x-1)² = 0  

(1-x)² = 0    

x = 1

x = 1

Answer 2

To simplify the expression (3x - 8x²) / (x - 1)² + (2x² + 3x³) / (1 - x)², you can start by factoring both denominators and then find a common denominator. Here are the steps:

Step 1: Factor the denominators.

1. Factor (x - 1)²: (x - 1)² = x² - 2x + 1
2. Factor (1 - x)²: (1 - x)² = (1 - x)(1 - x) = 1 - 2x + x²

Step 2: Find a common denominator. The common denominator will be the least common multiple of the two factored denominators, which is (x - 1)² * (1 - x)².

Step 3: Rewrite the fractions with the common denominator. (3x - 8x²) / (x - 1)² + (2x² + 3x³) / (1 - x)²

Now, rewrite these fractions with the common denominator: [(3x - 8x²)(1 - x)² + (2x² + 3x³)(x - 1)²] / [(x - 1)² * (1 - x)²]

Step 4: Expand and simplify the numerators. Expand both numerators: Numerator 1: (3x - 8x²)(1 - x)² = (3x - 8x²)(1 - 2x + x²) = 3x - 6x² + 3x³ - 8x² + 16x³ - 8x⁴ Numerator 2: (2x² + 3x³)(x - 1)² = (2x² + 3x³)(x² - 2x + 1) = 2x⁴ - 4x³ + 2x² + 3x⁵ - 6x⁴ + 3x³

Now, combine the two numerators: Numerator = (3x - 6x² + 3x³ - 8x² + 16x³ - 8x⁴) + (2x⁴ - 4x³ + 2x² + 3x⁵ - 6x⁴ + 3x³)

Step 5: Combine like terms in the numerator. Numerator = (3x³ + 3x³ - 4x³ + 16x³) + (-8x⁴ - 6x⁴ + 2x⁴) + (-6x² + 2x²) + (3x⁵)

Numerator = 18x³ - 12x⁴ - 4x² + 3x⁵

Step 6: Rewrite the expression with the simplified numerator and common denominator. [18x³ - 12x⁴ - 4x² + 3x⁵] / [(x - 1)² * (1 - x)²]

So, the simplified expression is: [18x³ - 12x⁴ - 4x² + 3x⁵] / [(x - 1)² * (1 - x)²]