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The denominator of a rational number is 3 more than the numerator. If 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/4. what is the rational what is the rational number​

Answer 1

Answer:

• $\frac{1}{2}$

Step-by-step explanation:

Let us assume the numerator to be 'x'

According to the first half of the question, it is clearly mention that the denominator of the given expression is 3 more than the numerator ;hence the equation to this part is :$\frac{x}{3+x}$

Now, according to the second half of the question, it is mentioned that if we subtract 1 from both numerator and denominator, the final answer to question will be $\frac{1}{4}$

Therefore the equation to this part is : $\frac{x-1}{2+x}=\frac{1}{4}$

No solving the question, we get :

$\frac{x - 1}{2 - x} = \frac{1}{4} \\ \\ 4(x - 1) = 1(2 - x) \\ 4x - 4 = 2 - 2x \\ 4x - 2x = 4 + 2 \\ 2x = 6 \\ x = 3$

Conclusion : the value of 'x' is 3

And the rational numbers in the half of the question is $\frac{3}{6}=\frac{1}{2}$.