# Algebraic expression simplification 2(2u+v)/u = 4(v^2-4u^2)/3u^2

• MHB
• Nightspider
In summary, the expression 2(2u+v)/u = 4(v^2-4u^2)/3u^2 simplifies to 3u = 2(v-2u) and this is true only if v+2u ≠ 0. The right hand side of the equation can be expressed as 4(v-2u)(v+2u) through the difference of two squares.
Nightspider
Hi All

I am trying to simplify an algebraic expression, I know what the expression should simplify to but I am struggling to simplify it.

The expression is: 2(2u+v)/u = 4(v^2-4u^2)/3u^2

and it is supposed to simplify to: 3u = 2(v-2u)

I have approached this problem from various angles by rearranging the expression and factorization but I can't seem to simplify it. Any pointers would be greatly appreciated. This is my first time posting on a forum so if I have not followed any of the rules of the forum please advise me. In the interest of transparency this is part of an assignment question from a module in a part time Physics degree I am doing as a mature student. For the purposes of this assignment I believe the important thing is to understand the Physics hence the fact that I am asking for some help with the math's. That being said I spent a significant amount of time trying to understand the math's before posting here.

Many Thanks

Nightspider said:
Hi All

I am trying to simplify an algebraic expression, I know what the expression should simplify to but I am struggling to simplify it.

The expression is: 2(2u+v)/u = 4(v^2-4u^2)/3u^2

and it is supposed to simplify to: 3u = 2(v-2u)

I have approached this problem from various angles by rearranging the expression and factorization but I can't seem to simplify it. Any pointers would be greatly appreciated. This is my first time posting on a forum so if I have not followed any of the rules of the forum please advise me. In the interest of transparency this is part of an assignment question from a module in a part time Physics degree I am doing as a mature student. For the purposes of this assignment I believe the important thing is to understand the Physics hence the fact that I am asking for some help with the math's. That being said I spent a significant amount of time trying to understand the math's before posting here.

Many Thanks

So we have, $\dfrac{2(v + 2u)}{u} = \dfrac{4(v^2-4u^2)}{3u^2}$. If we multiply both sides by $3u^2$ we obtain,

$6u(v + 2u)= 4(v^2-4u^2)$.

Now the right hand side can be expressed as: $4(v^2 - (2u)^2) = 4(v - 2u)(v + 2u)$. This is called the difference of two squares, and when first starting out, it isn't necessarily an obvious step.

Continuing,

$6u(v + 2u)= 4(v - 2u)(v + 2u)$,

now if we divide by $2(v + 2u)$ we arrive at,

$3u = \dfrac{\cancelto{2}{4}(v - 2u) \cancel{(v + 2u)}}{\cancel{2} \cancel{(v + 2u)}}$ which is desired expression,

$3u = 2(v - 2u)$.

Notice that this equivalence is true only if $$\displaystyle v+ 2u\ne 0$$.

Brilliant many thanks. Seems easy once someone who knows how shows you but I spent quite some time looking at it. Your swift reply is very much appreciated.

Thank You

$7u=2v$

## 1. What is an algebraic expression?

An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

## 2. How do you simplify an algebraic expression?

To simplify an algebraic expression, you need to combine like terms, use the distributive property, and perform any necessary operations to simplify the expression as much as possible. The goal is to get the expression in its simplest form, with no parentheses or like terms remaining.

## 3. What does "2(2u+v)/u" mean in the given expression?

The notation "2(2u+v)/u" means to multiply the entire expression inside the parentheses by the number 2, and then divide the result by the variable u. This can also be written as 2 * (2u+v) / u.

## 4. What is the purpose of simplifying an algebraic expression?

The purpose of simplifying an algebraic expression is to make it easier to work with and understand. Simplifying can also help to identify patterns and relationships between different terms in the expression.

## 5. How do you solve the given algebraic expression?

To solve the given expression, you need to simplify it first by combining like terms and using the distributive property. Once the expression is simplified, you can solve for the variable u or v by isolating it on one side of the equation. This can be done by performing inverse operations, such as dividing by a number or subtracting a term from both sides of the equation.

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