Question

Чи є число 4 коренем рівняння: x²-3x/x-4 = x²-x/4-x. Дати відповідь з поясненням.

Answer 1

To simplify the given expression, let's first find a common denominator for the fractions:

x² - (3x)/(x - 4) = x² - x/(4 - x)

The common denominator is (x - 4)(4 - x). Multiplying each term by the common denominator:

(x² - (3x)/(x - 4)) * (4 - x) = (x² - x)/(4 - x)

Expanding and simplifying:

(x² - 3x) * (4 - x) = (x² - x)

Now, let's simplify further:

4x² - x³ - 12x + 3x² = x² - x

Rearranging the terms:

x³ + x² - 7x = 0

Now the expression is simplified to the equation x³ + x² - 7x = 0.