# How to Solve Fractional Equations with Squared Variables?

• homegrown898
In summary: Just divide both sides by -4 and you'll get the solution.In summary, the conversation was about solving a math problem involving fractions and simplifying the equation. The participants discussed using LCD (least common denominator) and expanding the equation to solve for the unknown variable. The conversation also touched on the topic of using LaTeX to write mathematical expressions. The final solution was -x/2 = -3/2, after dividing both sides by -4.
homegrown898
Because I can't write squared, if x is squared, I will just write it like this: xsquared

x/x +2 MINUS x/xsquared - 4 = x+3/x+2

I get an LCD for each fracton and then I subtract getting this:

xsquared - 2x MINUS x/xsquared - 4 = (x+3)(x-2)/xsquared - 4

What do I do now?

If you don't understand this just ask me to scan it

I suppose you mean

$$\frac{x}{x+2} - \frac{x}{x^2-4} = \frac{x+3}{x+2} \Longrightarrow \frac{x^2 - 3x}{x^2 - 4} = \frac{(x+3)(x-2)}{x^2 - 4}$$

which is fine.

Last edited:
homegrown898 said:
If you don't understand this just ask me to scan it
Or just learn LaTeX.

I'm not quite sure what you mean. I surmise it is something like this:

$$\frac{x}{x+2}-\frac{x}{x^2-4}=\frac{x+3}{x+2}$$

If it's not right, let me know.

EDIT: Yarr, Data got there before I did...

Data said:
I suppose you mean

$$\frac{x}{x+2} - \frac{x}{x^2-4} = \frac{x+3}{x+2} \Longrightarrow \frac{x^2 - x}{x^2 - 4} = \frac{(x+3)(x-2)}{x^2 - 4}$$

which is fine.

Moo, that was right what you posted

And that is where I got but the instructions are to solve

Is that a solution to it?

Note that there is a small error in the thing you quoted, which I've corrected now.

To solve, multiply $x^2-4$ through both sides, expand on the right, and see what you get.

Data said:
Note that there is a small error in the thing you quoted, which I've corrected now.

To solve, multiply $x^2-4$ through both sides, expand on the right, and see what you get.

I don't want to learn Latex right now because it will take too long but I'll learn it for the future.

This is what I'm getting:

xsquared - 2x - x = xsquared + x - 6

I subtract xsquared on each side to cancel them out getting:

-2x - x = x - 6

I then subract x from each side getting

-3x - x = -6

Then I subract the x

-4x = -6

Did I mess up?

homegrown898 said:
Did I mess up?
Looks right to me.

## What is a fractional equation?

A fractional equation is an equation that contains fractions or rational expressions. These equations can be solved by isolating the variable on one side of the equation and then simplifying the fractions using common denominators.

## How do you solve a fractional equation?

To solve a fractional equation, begin by isolating the variable on one side of the equation. Next, use the cross-multiplication method to eliminate the fractions and solve for the variable. Finally, check your solution by plugging it back into the original equation.

## What are some common mistakes when solving fractional equations?

One common mistake when solving fractional equations is forgetting to check for extraneous solutions. This can occur when multiplying both sides of the equation by a variable that could potentially be equal to zero. It is important to check the final solution by plugging it back into the original equation to ensure it is valid.

## Can fractional equations have more than one solution?

Yes, fractional equations can have more than one solution. However, it is important to check for extraneous solutions and to state the domain of the solution set when solving these equations.

## What are some real-life applications of fractional equations?

Fractional equations are used in many real-life applications, such as calculating medication dosages, solving gas laws in chemistry, and determining the speed of an object in physics. They are also useful in budgeting and financial planning, as well as in engineering and construction projects.

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