2xsquare -8x -42 over 6xsquare divided by xsquare -9 over xsquare -3x in simplist form
To simplify the expression, let's break down each term and then simplify the division.
Expression: (2x^2 - 8x - 42) / (6x^2) ÷ (x^2 - 9) / (x^2 - 3x)
Step 1: Factorize numerator and denominator separately.
Numerator: 2x^2 - 8x - 42
= 2(x^2 - 4x - 21)
= 2(x - 7)(x + 3)
Denominator: 6x^2
= 2(3x)^2
= 2(9x^2)
Step 2: Cancel out common factors between the numerator and denominator.
(2(x - 7)(x + 3)) / (2(9x^2)) ≡ (x - 7)(x + 3) / (9x^2)
Step 3: Factorize the other part of the expression in the same manner.
Numerator: x^2 - 9
= (x - 3)(x + 3)
Denominator: x^2 - 3x
= x(x - 3)
Step 4: Perform the division by multiplying the numerator with the reciprocal of the denominator.
((x - 7)(x + 3) / (9x^2)) * ((x - 3)(x + 3) / (x(x - 3)))
Step 5: Cancel out the common factors between the numerator and denominator.
((x - 7) / (9x^2)) * ((x + 3) / (x))
Final Simplified Form: (x - 7)(x + 3) / (x * 9x^2)
= (x - 7)(x + 3) / (9x^3)