Question

&
The numerator of the fraction is
3 less then the demomenter. If 4 is
added to both numerator and
denominator the value of the fraction
increase by & Find the fraction.
by using quadretic formula
​

Answer 1

Answer:

We also know that when you have the same numerator and denominator in a fraction, it always equals 1. For example: So as long as we multiply or divide both the top and the bottom of a fraction by the same number, it's just the same as multiplying or dividing by 1 and we won't change the value of the fraction.

Step-by-step explanation:

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Answer 2

AnswEr :

• The original fraction is 5/8.

Step-by-step explanation :

We are given that numerator of a fraction is 3 less than the denominator and if 4 is added to both numerator and denominator, the value of the fraction increases by 1/8 .

SoluTion :

Let us assume that the denominator is x.

As it is given that numerator of a fraction is 3 less than its denominator .

New fraction will be = $\sf\dfrac{x - 3}{x}$

Now, according to the question, let's form the equation for further value,

$\implies \sf \: \: \: \dfrac{x - 3 + 4}{x + 4} = \dfrac{x - 3}{ x } + \dfrac{1}{8}$

$\implies \sf \: \: \: \dfrac{x + 1}{x + 4} = \dfrac{8(x - 3) + 1x}{ 8 \times x}$

$\implies \sf \: \: \: \dfrac{x + 1}{x + 4} = \dfrac{8x - 24 + x}{ 8 x}$

$\implies \sf \: \: \: \dfrac{x + 1}{x + 4} = \dfrac{9x - 24}{ 8 x}$

$\implies \sf \: \: \: 8x(x +1) = x + 4(9x - 24)$

$\implies \sf \: \: \: {8x}^{2} + 8x = {9x}^{2} - 24x + 36x - 96$

$\implies \sf \: \: \: {8x}^{2} + 8x = {9x}^{2} + 12x - 96$

$\implies \sf \: \: \: - {x}^{2} - 4x + 96 = 0$

$\implies \sf \: \: \: {x}^{2} + 4x - 96 = 0 \: \: \: \: \: \: \: \: \: \: \: \: (sign \: convention )$

$\implies \sf \: \: \: {x}^{2} + 12x - 8x - 96 = 0$

$\implies \sf \: \: \: x(x + 12) - 8(x + 12) = 0$

$\implies \sf \: \: \: (x + 12) (x - 8) = 0$

$\implies \sf \: \: \: { \blue{ x = - 12 \: \: or \: \: x = 8 }}$

• 1st case (x = -12)

$\sf : \implies \: \: \: \dfrac{x - 3}{x}$

$\sf : \implies \: \: \: \dfrac{ - 12 - 3}{ - 12}$

$\sf : \implies \: \: \: \dfrac{ - 15}{ - 12}$

$\sf : \implies \: \: \: { \boxed{ \sf{ \: \dfrac{ 5}{ 4} \: }}} \: \bigstar$

5/4 doesn't satisfy the equation as it is given that numerator of a fraction is 3 less than its denominator .

• Case 2 (x = 8)

$\sf : \implies \: \: \: \dfrac{x - 3}{x}$

$\sf : \implies \: \: \: \dfrac{8 - 3}{8}$

$\sf : \implies \: \: \: { \boxed{ \sf{ \: \: \dfrac{5}{8} \: }}} \: \bigstar$

5/8 satisfies the equation as it is given that numerator of a fraction is 3 less than its denominator .

So, the original fraction is 5/8 .