Question

3(x+1/x^2)-7(1+1/x)=0​

Answer 1

Детали на фото. 3(x+1/{x^2})-7(1+1/x)=3({x^3+1}/{x^2})-7({x+1}/x)

Answer 2

To solve the equation 3(x + 1/x^2) - 7(1 + 1/x) = 0, let's simplify and solve step by step:

Step 1: Expand the terms: 3x + 3/x^2 - 7 - 7/x = 0

Step 2: Combine like terms: (3x - 7) + (3/x^2 - 7/x) = 0

Step 3: To simplify the equation further, we can find a common denominator for the fraction: (3x - 7) + (3x - 7)/x^2 = 0

Step 4: Multiply the second term by x/x to get a common denominator: (3x - 7) + (3x^3 - 7x)/x^2 = 0

Step 5: Combine the fractions: (3x - 7 + 3x^3 - 7x)/x^2 = 0

Step 6: Combine like terms in the numerator: (3x^3 + 3x - 7x - 7)/x^2 = 0

Step 7: Simplify the numerator: (3x^3 - 4x - 7)/x^2 = 0

Step 8: Now, we have a rational expression equal to zero. To solve it, we can set the numerator equal to zero: 3x^3 - 4x - 7 = 0

At this point, we have a cubic equation, which can be challenging to solve algebraically. In some cases, it may require numerical methods or approximations to find the solutions.