Question

4²/x²+5x-3/x²-5x=7/x​

Answer 1

3x²- 4x + 7 = x² - 5x + (-1 + 2x²)

3x² - 4x + 7 = x² - 5x - 1 + 2x²

3x² - 4x + 7 = 3x² - 5x - 1

-4x + 7 = -5x - 1

5x - 4x = -1 - 7

x = -8

Answer 2

To solve the equation (4²/x²) + (5x - 3/x²) - (5x) = 7/x, we can follow these steps:

Step 1: Simplify the equation by getting rid of the fractions. Multiply the entire equation by x² to eliminate the denominators: (4²) + (5x - 3) - (5x)(x²) = 7

Step 2: Simplify further by expanding and combining like terms: 16 + 5x - 3 - 5x³ = 7

Step 3: Rearrange the equation to set it equal to zero: -5x³ + 5x + 10 = 0

Step 4: Divide the equation by -5 to simplify further: x³ - x - 2 = 0

Now, we can use various methods to solve this cubic equation. One approach is to factorize it if possible. In this case, we observe that x = 2 is a solution.

Step 5: Divide the cubic equation by (x - 2) to obtain the quadratic equation: (x - 2)(x² + 2x + 1) = 0

Step 6: Solve the quadratic equation x² + 2x + 1 = 0 using factoring or the quadratic formula: (x + 1)(x + 1) = 0 (x + 1)² = 0

Step 7: Solve for x: x + 1 = 0 x = -1

Therefore, the solutions to the equation are x = 2 and x = -1.