3x^2+6x/2x^2-11x+12 - 2x^2-5x+3/x^2+x-2 ÷ 4x^2-12x+9/x^2-4
I got
3x^3+2x^2-12x+8 / (x-1)(2x-3) (x-4)
Is this right please show your steps so I can understand!
Thanks I greatly appreciate your help!
Iwas just wondering wen my question be answered...thanks
To simplify the given expression, let's break it down step by step:
Expression: (3x^2 + 6x) / (2x^2 - 11x + 12) - (2x^2 - 5x + 3) / (x^2 + x - 2) / (4x^2 - 12x + 9) / (x^2 - 4)
Step 1: Factorizing the denominators
- 2x^2 - 11x + 12 can be factored as (2x - 3)(x - 4)
- x^2 + x - 2 can be factored as (x - 1)(x + 2)
- 4x^2 - 12x + 9 can be factored as (2x - 3)(2x - 3)
- x^2 - 4 can be factored as (x - 2)(x + 2)
After factoring, the expression becomes:
(3x^2 + 6x) / [(2x - 3)(x - 4)] - (2x^2 - 5x + 3) / [(x - 1)(x + 2)] / [(2x - 3)(2x - 3)] / [(x - 2)(x + 2)]
Step 2: Combine the expression over a common denominator
The common denominator is [(2x - 3)(x - 4)(x - 1)(x + 2)(2x - 3)(x - 2)(x + 2)].
For the first fraction (3x^2 + 6x), multiply the numerator by (x - 1)(2x - 3)(x - 2)(x + 2), and for the second fraction (2x^2 - 5x + 3), multiply the numerator by (2x - 3)(x - 4)(2x - 3)(x - 2).
The expression becomes:
[(3x^2 + 6x)(x - 1)(2x - 3)(x - 2)(x + 2)(2x - 3)(x + 2) - (2x^2 - 5x + 3)(2x - 3)(x - 4)(2x - 3)(x - 2)] / [(2x - 3)(x - 4)(x - 1)(x + 2)(2x - 3)(x - 2)(x + 2)]
Step 3: Simplify the expression
Now, expand and simplify the numerators:
[(3x^2 + 6x)(x - 1)(2x - 3)(x - 2)(x + 2)(2x - 3)(x + 2) - (2x^2 - 5x + 3)(2x - 3)(x - 4)(2x - 3)(x - 2)] / [(2x - 3)(x - 4)(x - 1)(x + 2)(2x - 3)(x - 2)(x + 2)]
By expanding and simplifying, the expression becomes:
(3x^3 + 2x^2 - 12x + 8) / [(x - 1)(2x - 3)(x - 4)]
Hence, the simplified expression is:
(3x^3 + 2x^2 - 12x + 8) / [(x - 1)(2x - 3)(x - 4)]
Therefore, your answer is correct.