Transform the Fraction Equation: Simplifying 1 + y/x + x/4y = 0

Consider the following relationship between x and y:

$1+\frac{y}{x}+\frac{x}{4y}=0$

Express the equation in the form of a reduced multiplication formula.

Video Solution

Solution Steps

00:00 Display the equation as a shortened multiplication formula

00:04 Multiply by the common denominator to eliminate fractions

00:31 Use the commutative law and arrange the equation

00:39 Factor the expression

00:49 Use the shortened multiplication formulas to find the parentheses

00:57 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's work through these steps:

Step 1: Start with the given equation: $1+\frac{y}{x}+\frac{x}{4y}=0$ .
Step 2: Clear the fractions by multiplying all terms by $4xy$ , the common denominator.
Step 3: This gives us: $4xy + 4y^2 + x^2 = 0$ .
Step 4: Rearrange the terms for clarity: $x^2 + 4xy + 4y^2 = 0$ .
Step 5: Recognize this as the perfect square: $(x + 2y)^2 = 0$ .

This simplification results in the equation: $(x+2y)^2 = 0$ .

Therefore, the solution to the problem is $(x+2y)^2 = 0$ .