The numerator of a fraction is multiple of two numbers.

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The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7 + c (c > –7) is a constant, then the minimum value of the fraction is

Let the first number be x.
∴ Second number = x + 2
According to the question,
x + 2 = 7 + c – 4 = 3 + c
⇒ x = 1 + c
∴ Fraction

=	x(x + 2)	=	(1 + c) (3 + c)
	7 + c		7 + c

For the minimum value,
–3 < c < –1
∴ c = –2
∴ Required value of fraction = –

∴ Required value of fraction = –	1
	5