The value of a certain fraction becomes 1/5 if one is added to its numerator. if one is taken away from its denominator, its value becomes 1/7. find the fraction.
use an algebraic equation.

Step-by-step explanation:

Let the original fraction be

Then adding 1 to the numerator gives

= ( cross-  multiply )

⇒ y = 5x + 5 → (1)

Subtracting 1 from the denominator gives

= (cross-  multiply )

y - 1 = 7x → (2)

Substitute y = 5x + 5 into (2)

5x + 5 - 1 = 7x ← subtract 5x from both sides

4 = 2x ⇒ x = 2

Substitute x = 2 into (1)

y = (5 × 2) + 5 = 10 + 5 = 15

Hence original fraction =

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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