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

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

 ` `

## Javascript

 ` `

Output:

`?X = 6`

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

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