4n² - 15n + 14<span> is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.
Case n - 2 = 1
That would be n = 3
Then </span>4n² - 15n + 14<span> = 5 , which is prime.
Case n - 2 = -1
That would be n = 1
Then </span>4n<span>² - 15n + 14 = 3, which is also prime.
Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime
Case 4n-7 = -1
That would be n = 3/2 which is not integer, so </span>4n<span>² - 15n + 14 will not be interger.
For any other n values, </span>4n<span>² - 15n + 14 will be composite number since it is product of two factors.
Therefore we are left with n = 1 and n = 3; only two values of n.</span>
Convert the denominator of the first two fractions to 24 since 3 and 8 can fit into 24.
3/8=9/24
2/3=16/24
Now add them together.
9/24+16/24=25/24
Next add the second two fractions 9/24 and 16/24.
9/24+16/24=25/24
Since all fractions equal 25/24, the equation was true!
Hope this helps!
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