# 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 ΔX 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 : ΔX = 2 Explanation : (a + ΔX)/(b + ΔX) = (4 + 2) / (10 + 2) = 6/12 = 1/2 = c/d Input : a = 4, b = 10, c = 2, d = 5 Output : ΔX = 0 Explanation : (a + ΔX) / (b + ΔX) = (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 ΔX such that: => (a + ΔX) / (b + ΔX) = c / d => ad + dΔX = bc + cΔX => dΔX - cΔX = bc - ad => ΔX (d - c) = bc -ad => ΔX = (bc - ad) / (d - c)

So, in a way to finding ΔX we have to only calculate .

## C++

`// C++ Program to find deltaX` `#include <bits/stdc++.h>` `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

`<?php` `// PHP Program to find deltaX` `// function to find delta X` `function` `findDelta(` `$a` `, ` `$b` `,` ` ` `$c` `, ` `$d` `)` `{` ` ` `return` `(` `$b` `* ` `$c` `-` ` ` `$a` `* ` `$d` `) / (` `$d` `- ` `$c` `);` `}` `// Driver Code` `$a` `= 3; ` `$b` `= 9;` `$c` `= 3; ` `$d` `= 5;` `// u0394X is code for delta sign` `echo` `"?X = "` `.findDelta(` `$a` `, ` `$b` `,` ` ` `$c` `, ` `$d` `);` `// This code is contributed by` `// Manish Shaw(manishshaw1)` `?>` |

## Javascript

`<script>` `// JavaScript Program to` `// find deltaX` ` ` `// function to find delta X` ` ` `function` `findDelta(a, b, c, d)` ` ` `{` ` ` `return` `(b * c - a *` ` ` `d) / (d - c);` ` ` `}` ` ` `// Driver Code` ` ` `let a = 3, b = 9,` ` ` `c = 3, d = 5;` ` ` ` ` `// u0394X is code` ` ` `// for delta sign` ` ` `document.write(` `"\u0394X = "` `+` ` ` `findDelta(a, b, c, d));` `// This code is contributed by splevel62.` `</script>` |

**Output:**

ΔX = 6

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