# Find ΔX which is added to numerator and denominator both of fraction (a/b) to convert it to another fraction (c/d)

Last Updated : 20 Feb, 2023

Given a fraction in form of a/b where a & b are positive integers. Find ?X such that when it is added to numerator as well as denominator of given fraction it will result into a new Ir-reducible fraction c/d.
Examples:

```Input : a = 4, b = 10, c = 1, d = 2
Output : ?X = 2
Explanation : (a + ?X)/(b + ?X) =
(4 + 2) / (10 + 2) = 6/12 = 1/2 = c/d

Input : a = 4, b = 10, c = 2, d = 5
Output : ?X = 0
Explanation : (a + ?X) / (b + ?X) =
(4) / (10) = 2 / 5 = c/d```

To solve this type of problem rather than implementing just a programming approach we have to do a little of mathematics. mathematics just necessary is as:

```As per question we have to find ?X such that:
=> (a + ?X) / (b + ?X) = c / d
=> ad + d?X = bc + c?X
=> d?X - c?X = bc - ad
=> ?X (d - c) = bc -ad
=> ?X = (bc - ad) / (d - c)```

So, in a way to finding ?X we have to only calculate

## C++

 `// C++ Program to find deltaX ``#include ``using` `namespace` `std; `` ` `// function to find delta X ``int` `findDelta(``int` `a, ``int` `b, ``int` `c, ``int` `d) ``{ ``    ``return` `(b * c - a * d) / (d - c); ``} `` ` `// driver program ``int` `main() ``{ ``    ``int` `a = 3, b = 9, c = 3, d = 5; `` ` `    ``// u0394X is code for delta sign ``    ``cout << ``"\u0394X = "` `<< findDelta(a, b, c, d); ``    ``return` `0; ``} `

## Java

 `// Java Program to ``// find deltaX ``import` `java.io.*; `` ` `class` `GFG ``{ ``    ``// function to find delta X ``    ``static` `int` `findDelta(``int` `a, ``int` `b,  ``                         ``int` `c, ``int` `d) ``    ``{ ``        ``return` `(b * c - a *  ``                ``d) / (d - c); ``    ``} ``     ` `    ``// Driver Code ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``int` `a = ``3``, b = ``9``,  ``            ``c = ``3``, d = ``5``; ``     ` `        ``// u0394X is code  ``        ``// for delta sign ``        ``System.out.print(``"\u0394X = "` `+  ``                ``findDelta(a, b, c, d)); ``    ``} ``} `` ` `// This code is contributed  ``// by Manish Shaw(manishshaw1) `

## Python3

 `# Python Program to find deltaX ``# !/usr/bin/python ``# coding=utf-8 `` ` `# function to find delta X ``def` `findDelta(a, b, c, d) : `` ` `    ``return` `int``((b ``*` `c ``-``                ``a ``*` `d) ``/` `               ``(d ``-` `c)); `` ` `# Driver Code ``a ``=` `3``; b ``=` `9``;  ``c ``=` `3``; d ``=` `5``; `` ` `# u0394X is code ``# for delta sign ``print` `(``"X = {}"` `.  ``        ``format``(findDelta(a, b,  ``                         ``c, d))); `` ` `# This code is contributed by  ``# Manish Shaw(manishshaw1) `

## C#

 `// C# Program to ``// find deltaX ``using` `System; `` ` `class` `GFG ``{ ``// function to find delta X ``static` `int` `findDelta(``int` `a, ``int` `b,  ``                     ``int` `c, ``int` `d) ``{ ``    ``return` `(b * c - a *  ``            ``d) / (d - c); ``} `` ` `// Driver Code ``static` `void` `Main() ``{ ``    ``int` `a = 3, b = 9,  ``        ``c = 3, d = 5; `` ` `    ``// u0394X is code  ``    ``// for delta sign ``    ``Console.Write(``"\u0394X = "` `+  ``                  ``findDelta(a, b, c, d)); ``} ``} `` ` `// This code is contributed  ``// by Manish Shaw(manishshaw1) `

## PHP

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## Javascript

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Output:

`?X = 6`

Time Complexity: O(1)
Auxiliary Space: O(1)