Question

1. 4+х/х-4 * (2х ^2/4+х - х) 2. у-3/у+3 * (у - у^2/у-3) 3. 4х-2/5у+10 : 2х-1/у+2

Answer 1

Данный ответ представлен фотографией.

Answer 2

Let's simplify each of the given expressions step by step:

1. $4+\frac{x}{x-4} \cdot \left(\frac{2x^2}{4+x} - x\right)$

   To simplify this expression, first, let's find a common denominator for the fractions inside the parentheses.

   $\frac{2x^2}{4+x}$ can be rewritten as $\frac{2x^2}{x+4}$.

   Now, we can rewrite the expression with a common denominator:

   $4+\frac{x}{x-4} \cdot \left(\frac{2x^2}{x+4} - x\right)$

   Next, distribute the $\frac{x}{x-4}$ term into the parentheses:

   $4+\frac{x \cdot 2x^2}{(x-4)(x+4)} - \frac{x^2}{x-4}$

   Now, let's simplify the fractions. To do that, find a common denominator:

   $4+\frac{2x^3}{(x-4)(x+4)} - \frac{x^2(x+4)}{(x-4)(x+4)}$

   Now, you have a common denominator, and you can combine the fractions:

   $4+\frac{2x^3 - x^2(x+4)}{(x-4)(x+4)}$

   To simplify the numerator further, expand $x^2(x+4)$:

   $4+\frac{2x^3 - x^3 - 4x^2}{(x-4)(x+4)}$

   $4+\frac{x^3 - 4x^2}{(x-4)(x+4)}$

2. $y-\frac{3}{y+3} \cdot \left(y - \frac{y^2}{y-3}\right)$

   First, let's find a common denominator for the fractions inside the parentheses:

   $y-\frac{3}{y+3} \cdot \left(y - \frac{y^2}{y-3}\right)$

   Now, distribute the $\frac{3}{y+3}$ term into the parentheses:

   $y - 3 \cdot \left(y - \frac{y^2}{y-3}\right)$

   Next, distribute the -3 inside the parentheses:

   $y - 3y + \frac{3y^2}{y-3}$

   Now, combine like terms:

   $-2y + \frac{3y^2}{y-3}$

3. $\frac{4x-2}{5y+10} : \frac{2x-1}{y+2}$

   To divide fractions, you can multiply by the reciprocal of the second fraction:

   $\frac{4x-2}{5y+10} \cdot \frac{y+2}{2x-1}$

   Simplify both the numerator and denominator:

   $\frac{2(2x-1)}{5(y+2)} \cdot \frac{y+2}{2x-1}$

   Now, you can cancel out the common factor of $2x-1$