To solve the equation 9x - 7/(3x - 2) - 7x - 5/(2x - 3) - 1 = 0, we first need to simplify the expression by finding a common denominator for the fractions.
The common denominator for 3x - 2 and 2x - 3 is (3x - 2)(2x - 3).
Now we rewrite the equation with the common denominator:
To solve the equation 9x - 7/(3x - 2) - 7x - 5/(2x - 3) - 1 = 0, we first need to simplify the expression by finding a common denominator for the fractions.
The common denominator for 3x - 2 and 2x - 3 is (3x - 2)(2x - 3).
Now we rewrite the equation with the common denominator:
9x(2x - 3) - 7(2x - 3)/(3x - 2)(2x - 3) - 7x(3x - 2) - 5/(3x - 2)(2x - 3) - 1 = 0
Expanding the equation further:
18x^2 - 27x - 14x + 21)/(3x - 2)(2x - 3) - 21x^2 + 14 - 5/(3x - 2)(2x - 3) - 1 = 0
Combining like terms, we get:
18x^2 - 41x + 35)/(3x - 2)(2x - 3) - 21x^2 + 9/(3x - 2)(2x - 3) - 1 = 0
Now we have a single fraction. We can combine it to simplify the equation:
(18x^2 - 41x + 35 - 63x^2 + 27)/(3x - 2)(2x - 3) - 1 = 0
Simplifying further, we get:
(-45x^2 - 14x + 62)/(3x - 2)(2x - 3) - 1 = 0
To solve for x, we need to set the equation equal to zero and solve for x:
(-45x^2 - 14x + 62)/(3x - 2)(2x - 3) = 1
(-45x^2 - 14x + 62)/(3x - 2)(2x - 3) = 1
-45x^2 - 14x + 62 = (3x - 2)(2x - 3)
Multiplying out the right side gives us:
-45x^2 - 14x + 62 = 6x^2 - 13x - 6
Subtract 6x^2 - 13x - 6 from both sides to set the equation equal to zero:
-51x^2 + 47x + 68 = 0
However, the quadratic equation -51x^2 + 47x + 68 = 0 cannot be factored easily, so you would need to use the quadratic formula to find the roots.