what is the number?

Question

four divided by the difference of a number and 2 minus 3 divided by a number plus 2, equal 3 times the reciprocal of the difference of the number squared and 4. What is the number?

Answer 1

Writing the algebra as it is read:

4 ÷ (n - 2) - 3 ÷ (n + 2) = 3 (1/(n² - 4)

 

Multiply both sides by (n² - 4). Note that the denominators shall reduce out.

 

4(n + 2) - 3(n - 2) = 3

4n + 8 - 3n + 6 = 3

n + 14 = 3

n = -11