Question

Which expression is equivalent to the expression below?

Answer 1

The expression which equivalent is 1/[(m - 4)(m - 3)] ⇒ 2nd answer

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)]

Answer 2

`(1)/((m-4)(m-3))`

Explanation:

The question requires you to simplify using quadratic identities

Re-write the numerator.

`(m+3)/(m^2-16) \\\\\\\\=(m+3)/((m+4)+(m-3) )`

Re-write the denominator as;

`((m+3) +(m-3))/(m+4)`

Re-arrange expression

`(m+3)/((m+4)+(m-4)) * (m+4)/((m+3)+(m-3))`

cancel the terms that are alike to remain with

`(1)/((m-4)(m-3))`