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!
To simplify the expression, let's break it down into smaller steps:
Step 1: Factor the numerators and denominators.
Numerator 1: 3x^2 + 6x
Common factor: 3x
Result: 3x(x + 2)
Numerator 2: -2x^2 - 5x + 3
This quadratic cannot be factored further.
Numerator 3: -2x^2 - 5x + 3
This quadratic cannot be factored further.
Denominator 1: 2x^2 - 11x + 12
Factors: (2x - 3)(x - 4)
Denominator 2: x^2 + x - 2
Factors: (x + 2)(x - 1)
Denominator 3: 4x^2 - 12x + 9
Factors: (2x - 3)(2x - 3)
Denominator 4: x^2 - 4
Factors: (x + 2)(x - 2)
Step 2: Rewrite the expression using the factored form.
Our expression becomes:
[3x(x + 2)] / [(2x - 3)(x - 4)] - [(-2x^2 - 5x + 3)] / [(x + 2)(x - 1)] ÷ [(4x^2 - 12x + 9)] / [(x + 2)(x - 2)]
Step 3: Simplify by canceling common factors.
We can cancel the common factors:
(x + 2), (2x - 3), and (x - 2)
After canceling, we are left with the following expression:
[3x] / [(x - 4)] - [(-2x^2 - 5x + 3)] / [(x - 1)] ÷ [(2x - 3)] / [(x + 2)]
Step 4: Simplify further if required.
There doesn't seem to be any further simplification possible for this expression.
So, the final simplified expression is:
[3x] / [(x - 4)] - [(-2x^2 - 5x + 3)] / [(x - 1)] ÷ [(2x - 3)] / [(x + 2)]