Question

The numerator of a fraction is 1less than the
donomination. If 3 is added to each of the
numerator and denominator, the fraction is
increased by 3/28. Find the fraction.​

Answer 1

Answer:

★ Fraction= ¾ ★

Step-by-step explanation:

Given:

• Numerator of a fraction is 1 less than denominator.
• After adding 3 to numerator & denominator the fraction is increased by 3/28

To Find:

• What is the fraction?

Solution: Let the denominator of fraction be x.

∴ Numerator will be x – 1

• Fraction = n/d = x – 1/x

★ Adding 3 to Numerator & Denominator

• Denominator = x + 3
• Numerator = x – 1 + 3 or x + 2

∴ Fraction will be n/d = x + 2/x + 3

A/q

$\small\implies{\sf }$ x + 2/x + 3 = x – 1/x + 3/28

$\small\implies{\sf }$ x + 2/x + 3 = 28x – 28 + 3x/28x

$\small\implies{\sf }$ x + 2/x + 3 = 31x – 28/28x

$\small\implies{\sf }$ 28x² + 56x = (31x – 28) ( x + 3 )

$\small\implies{\sf }$ 28x² + 56x = 31x² + 93x –28x – 84

$\small\implies{\sf }$ 28x² + 56x = 31x² +65x –84

$\small\implies{\sf }$ 0 = 31x² – 28x² + 65x – 56x –84

$\small\implies{\sf }$ 0 = 3x² + 9x –84

• Divide by 3 •

→ 3x²/3 + 9x/3 –84/3

→ x² + 3x –28

• By middle term splitting •

$\small\implies{\sf }$ x² + 7x – 4x –28

$\small\implies{\sf }$ x(x + 7) – 4(x + 7)

$\small\implies{\sf }$ (x – 4)( x + 7)

Here x = 4 or –7 [x is a natural number, x>0]

Therefore, Fraction will be

→ x –1/x

→ 4 –1/4

→ 3/4