Question

Сократить дробь: 4x-y ——— 2x-√xy

Answer 1

$= \frac{(2 \sqrt{x} - \sqrt{y})(2 \sqrt{x} + \sqrt{y} ) }{ \sqrt{ x }(2 \sqrt{x} - \sqrt{y} )} = \frac{2 \sqrt{x} + \sqrt{y} }{ \sqrt{x} }$

Answer 2

To simplify the given fraction (4x - y) / (2x - √xy), we'll try to find a common factor in both the numerator and denominator.

Step 1: Factor out common terms in the numerator and denominator if possible. The common factor between 4x - y and 2x - √xy is (2x - √xy).

Step 2: Divide both the numerator and denominator by the common factor. (4x - y) / (2x - √xy) = [(2x - √xy) * (2x + √xy)] / [(2x - √xy)]

Step 3: Cancel out the common factor. The (2x - √xy) terms in the numerator and denominator cancel out.

Step 4: Simplify the expression. The simplified fraction is: = 2x + √xy

So, the simplified form of the given fraction is 2x + √xy.