9x^3+5x-8/3x-2
To simplify the expression (9x^3 + 5x - 8) / (3x - 2), you can use polynomial long division. Here's how you can do it:
Step 1: Arrange the terms in descending order of exponents.
The original expression is: (9x^3 + 5x - 8) / (3x - 2)
Step 2: Divide the first term of the numerator by the first term of the denominator.
Divide 9x^3 by 3x to get 3x^2.
Step 3: Multiply the result from step 2 by the denominator and write it below the numerator.
Multiply (3x^2) by (3x - 2) to get (9x^3 - 6x^2).
Step 4: Subtract the result from step 3 from the numerator.
Subtract (9x^3 - 6x^2) from (9x^3 + 5x - 8) to get (11x^2 + 5x - 8).
Step 5: Repeat steps 2 to 4 until you can no longer divide.
Now, we have the expression (11x^2 + 5x - 8) / (3x - 2).
Step 6: Divide the first term of the numerator by the first term of the denominator.
Divide 11x^2 by 3x to get (11/3)x.
Step 7: Multiply the result from step 6 by the denominator and write it below the numerator.
Multiply ((11/3)x) by (3x - 2) to get ((11/3)x^2 - (22/3)x).
Step 8: Subtract the result from step 7 from the numerator.
Subtract ((11/3)x^2 - (22/3)x) from (11x^2 + 5x - 8) to get ((5/3)x + 8).
Step 9: Since the denominator (3x - 2) cannot be divided further, the final simplified expression is (3x^2 + (11/3)x + (5/3)).
Therefore, the simplified expression for (9x^3 + 5x - 8) / (3x - 2) is (3x^2 + (11/3)x + (5/3)).