Prove f(x + a)  f(x  a) = 2a/(a^2  x^2) if f(x) = 1/x  Summary and Q&A
TL;DR
Proving that f(x) plus a minus f(x) minus a is equal to 2A divided by a squared minus x squared.
Key Insights
 🎮 The video demonstrates how to manipulate and simplify equations using common denominators.
 🔨 The difference of squares formula is a useful tool in algebraic calculations.
 🤘 The solution showcases the cancellation of terms and the distribution of negative signs.
 🛀 The video emphasizes the importance of showing all steps in solving mathematical problems.
 💡 The content promotes the idea of practicing more mathematics to improve skills.
 ❓ It highlights the importance of understanding algebraic techniques and formulas.
 ❓ The solution verifies the desired equation using the provided steps.
Transcript
Below in this video we're going to do a mathematics problem let f of x equals 1 over X I'm going to show that f of x plus a minus f of x minus a is equal to 2A all divided by a squared minus x squared let's go ahead and carefully work through it solution let's start by writing down the left hand side of this equation so we have f of X plus a minus ... Read More
Questions & Answers
Q: What is the purpose of the video?
The video aims to teach viewers how to solve a specific mathematical equation involving f(x) and a.
Q: What is the equation being solved in the video?
The equation being solved is f(x) plus a minus f(x) minus a is equal to 2A divided by a squared minus x squared.
Q: What is the common denominator used in the equation?
The common denominator used is the product of (x + a) and (x  a).
Q: How is the difference of squares formula utilized in the solution?
The difference of squares formula is used to simplify the denominator of the equation, which becomes x squared minus a squared.
Summary & Key Takeaways

The video explains how to solve the equation f(x) plus a minus f(x) minus a equals 2A divided by a squared minus x squared.

It demonstrates stepbystep how to simplify and manipulate the equation to reach the desired solution.

The video emphasizes the use of the difference of squares formula and showcases various algebraic techniques.