Question

1 +( 3/(x + 1) )= 10/(x^2 + 2*x + 1) решить уравнение

Answer 1

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Answer 2

To solve the given equation:

1 + (3/(x + 1)) = 10/(x^2 + 2*x + 1)

First, let's simplify the equation by getting rid of the fractions. To do this, we'll start by finding a common denominator for the fractions on the left side:

The common denominator for (x + 1) and (x^2 + 2x + 1) is (x + 1) * (x + 1) = (x + 1)^2.

Now, we can rewrite the equation with the common denominator:

[(x + 1)^2 + 3]/(x + 1)^2 = 10/(x^2 + 2x + 1)

Next, we'll eliminate the denominators by cross-multiplying:

(x + 1)^2 + 3 = 10

Now, let's solve for x:

(x + 1)^2 = 10 - 3

(x + 1)^2 = 7

Now, we take the square root of both sides (remembering to consider both the positive and negative square roots):

x + 1 = ±√7

Now, isolate x by subtracting 1 from both sides:

x = -1 ± √7

So, the solutions to the equation are:

x = -1 + √7 and x = -1 - √7