simplify: [(2x^2+5x-6)/(5x^2+7x-6)]*[(20x^2-7x-3)/(6x^2-25x+4)]/[(4x^2-11x-3)/(6x^2-19x+3)]
Did you start the problem? You have to begin by factoring.
To simplify the given expression, we need to simplify both the numerator and the denominator, then divide the numerator by the denominator. Let's simplify each expression step-by-step:
1. Simplify the numerator:
Numerator: (2x^2 + 5x - 6) / (5x^2 + 7x - 6)
Factorize both numerator and denominator:
Numerator: [(x+3)(2x-1)] / [(5x-2)(x+3)]
2. Simplify the denominator:
Denominator: (20x^2 - 7x - 3) / (6x^2 - 25x + 4)
Factorize both numerator and denominator:
Denominator: [(4x+1)(5x-3)] / [(2x-1)(3x-4)]
3. Simplify the third expression:
Third expression: (4x^2 - 11x - 3) / (6x^2 - 19x + 3)
Factorize both numerator and denominator:
Third expression: [(4x+1)(x-3)] / [(3x-1)(2x-3)]
Now, let's substitute these simplified expressions back into the original expression:
[(x+3)(2x-1) / (5x-2)(x+3)] * [(4x+1)(5x-3) / (2x-1)(3x-4)] / [(4x+1)(x-3) / (3x-1)(2x-3)]
Next, we can cancel out similar factors in the numerator and denominator:
[(2x-1)(5x-3) / (5x-2)(3x-4)] * [(3x-1)(2x-3) / (x-3)]
Now we multiply the numerators together and the denominators together:
[(2x-1)(5x-3)(3x-1)(2x-3)] / [(5x-2)(3x-4)(x-3)]
This is the simplified form of the given expression.