perform the indicated operation and simplify:
3x+6 x^2-4
----- divided by -----
4x+12 x-3
(3x+6)/(4x+12) / (x^2 - 4)/(x-3)
first, to divide, we get the reciprocal of the divisor (or the second term/ term at the right) and the operation will be multiplication. reciprocal is just interchanging the numerator and denominator terms. thus,
(3x+6)/(4x+12) * (x-3)/(x^2 - 4)
factoring out each term,
[3(x+2)]/[4(x+3)] * (x-3)/[(x-2)(x+2)]
we can cancel out x+2:
[3(x-3)]/[4(x+3)(x-2)] or
(3x - 9)/(4x^2 + 4x - 24)
hope this helps~ :)
To perform the indicated operation and simplify the expression, you need to divide the numerator by the denominator. Follow these steps to get the answer:
Step 1: Factorize the polynomials in both the numerator and denominator.
The numerator can be factored as: 3(x + 2)
The denominator can be factored as: 4(x + 3)
Step 2: Rewrite the expression with the factored form:
(3(x + 2))/(4(x + 3))
Step 3: Simplify the expression by canceling out common factors, if possible.
In this case, we can cancel out the common factor of (x + 2):
(3)/(4(x + 3))
Thus, the simplified form of the expression (3x + 6)/(4x + 12) รท (x^2 - 4)/(x - 3) is:
(3)/(4(x + 3))
Note that the expression is simplifed as much as possible, considering the common terms and factors.