Answer:
The expression which equivalent is 1/[(m - 4)(m - 3)] ⇒ 2nd answer
Step-by-step explanation:
* Lets revise how to divide two fractions
- To divide a/b and c/d change the division operation to multiplication
operation and reciprocal the fraction after the division sign
# a/b ÷ c/d = a/b × d/c
* Lets solve the problem
∵ (m + 3)/(m² - 16) ÷ (m² - 9)/(m + 4)
- Use the factorization to simplify the fractions
∵ m² - 16 is a different of two squares
- The factorization of the different of two squares a² - b² is
∵ a² = a × a , -b² = b × -b
∴ a² - b² = (a + b)(a - b)
- Use this way with m² - 16
∵ m² = m × m
∵ -16 = 4 × -4
∴ m² - 16 = (m + 4)(m - 4)
- Similar factorize m² - 9
∵ m² = m × m
∵ -9 = 3 × -3
∴ m² - 9 = (m + 3)(m - 3)
- Now lets write the fraction and simplify it
∵ (m + 3)/(m² - 16) ÷ (m² - 9)/(m + 4)
∴ (m + 3)/[(m + 4)(m - 4)] ÷ [(m + 3)(m - 3)]/(m + 4)
- Change the division operation to multiplication operation and
reciprocal the fraction after the division sign
∴ (m + 3)/[(m + 4)(m - 4)] × (m + 4)/[(m + 3)(m - 3)]
- We can cancel (m + 4) in the denominator of the first fraction with
(m + 4) in the numerator of the second fraction and cancel (m + 3)
in the numerator of the first fraction with (m + 3) in the denominator
of the second fraction
∴ 1/(m - 4) × 1/(m - 3) ⇒ multiply the two fractions
∴ 1/[(m - 4)(m - 3)]
* The expression which equivalent is 1/[(m - 4)(m - 3)]
