Question

9х-7/3х-2 - 4х-5/2х-3 = 1​

Answer 1

Решение на фото

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Answer 2

To solve the equation, we need to find the value of "x" that makes the equation true. Let's first simplify the equation by combining like terms and getting rid of the fractions. Then we can solve for "x".

Given equation:

(9x - 7) / (3x - 2) - (4x - 5) / (2x - 3) = 1

Step 1: Find a common denominator for both fractions, which is (3x - 2)(2x - 3):

[(9x - 7)(2x - 3) - (4x - 5)(3x - 2)] / [(3x - 2)(2x - 3)] = 1

Step 2: Expand the numerator:

(18x^2 - 27x - 14x + 21) - (12x^2 - 8x - 15x + 10) = (18x^2 - 27x - 14x + 21) - (12x^2 - 23x + 10) = 1

Step 3: Combine like terms:

18x^2 - 27x - 14x + 21 - 12x^2 + 23x - 10 = 1

Step 4: Continue combining like terms:

(18x^2 - 12x^2) + (-27x + 23x) + (-14x) + (21 - 10) = 1

6x^2 - 4x + 11 = 1

Step 5: Move all terms to one side of the equation to set it to zero:

6x^2 - 4x + 11 - 1 = 0

6x^2 - 4x + 10 = 0

Step 6: Divide the entire equation by 2 to simplify:

3x^2 - 2x + 5 = 0

Now, to find the values of "x", we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 3, b = -2, and c = 5.

Step 7: Plug in the values and calculate "x":

x = (2 ± √((-2)^2 - 4 * 3 * 5)) / 2 * 3

x = (2 ± √(4 - 60)) / 6

x = (2 ± √(-56)) / 6

As the value under the square root is negative, the solutions are complex numbers. The solutions for "x" are:

x = (2 + √56i) / 6 and x = (2 - √56i) / 6

Note: "i" is the imaginary unit, where i^2 = -1.