# Prove f(x + a) - f(x - a) = 2a/(a^2 - x^2) if f(x) = 1/x | Summary and Q&A

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June 7, 2023
by
The Math Sorcerer
Prove f(x + a) - f(x - a) = 2a/(a^2 - x^2) if f(x) = 1/x

## 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

### 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 step-by-step 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.