Question

(x*x+4x)/(x+7)=(5x+56)/(x+7)

Answer 1

Ответ:

8

Объяснение:

См. прикреплённый скриншот.

Домножим левую и правую части уравнения на (x + 7), тем самым избавившись от знаменателя. Перенесём всё в левую часть и приведём подобные. Решим квадратное уравнение.

Второй найденный корень (-7) не подходит, так как, если подставить его в знаменатель (x + 7), получаем 0, а на нуль делить нельзя!

Answer 2

To solve the equation $\frac{x^2+4x}{x+7}=\frac{5x+56}{x+7}$, you can start by noticing that both sides of the equation have a common denominator, which is $x+7$. Therefore, you can eliminate the denominators by multiplying both sides of the equation by $x+7$:

$(x+7) \cdot \frac{x^2+4x}{x+7} = (x+7) \cdot \frac{5x+56}{x+7}$

Now, you can cancel out the $x+7$ terms on both sides:

$x^2 + 4x = 5x + 56$

Next, bring all the terms to one side of the equation:

$x^2 + 4x - 5x - 56 = 0$

Now, combine like terms:

$x^2 - x - 56 = 0$

To factor the quadratic equation, you're looking for two numbers that multiply to -56 and add up to -1 (the coefficient of the $x$ term). Those numbers are -8 and 7:

$x^2 - 8x + 7x - 56 = 0$

Now, factor by grouping:

$x(x - 8) + 7(x - 8) = 0$

Notice that you have a common factor of $x - 8$:

$(x - 8)(x + 7) = 0$

Now, set each factor equal to zero and solve for $x$:

1. $x - 8 = 0$

$x = 8$

2. $x + 7 = 0$

$x = -7$

So, the solutions to the equation are $x = 8$ and $x = -7$.