Solve The Following Equation:${ \frac{y^2}{y+4} = \frac{16}{y+4} }$Select The Correct Choice Below And, If Necessary, Fill In The Answer Box To Complete Your Choice.A. The Solution(s) Is/are { \square$}$. (Type An Integer Or A

Introduction

In this article, we will be solving a quadratic equation that involves fractions. The equation is given as $\frac{y^2}{y+4} = \frac{16}{y+4}$. Our goal is to find the solution(s) to this equation, which will involve simplifying the equation, eliminating the fractions, and solving for the variable $y$.

Step 1: Simplifying the Equation

The first step in solving this equation is to simplify it by eliminating the fractions. We can do this by multiplying both sides of the equation by the denominator, which is $(y+4)$.

$\frac{y^2}{y+4} = \frac{16}{y+4}$

Multiplying both sides by $(y+4)$ gives us:

$y^2 = 16$

Step 2: Solving for $y$

Now that we have simplified the equation, we can solve for $y$. To do this, we need to isolate $y$ on one side of the equation. We can do this by taking the square root of both sides of the equation.

$y^2 = 16$

Taking the square root of both sides gives us:

$y = \pm \sqrt{16}$

Step 3: Simplifying the Square Root

The square root of $16$ is $4$, so we can simplify the equation as follows:

$y = \pm 4$

Conclusion

In conclusion, the solution to the equation $\frac{y^2}{y+4} = \frac{16}{y+4}$ is $y = \pm 4$. This means that the equation has two solutions: $y = 4$ and $y = -4$.

Final Answer

The final answer is: $\boxed{4, -4}$

Discussion

This equation is a quadratic equation that involves fractions. To solve it, we need to simplify the equation by eliminating the fractions, and then solve for the variable $y$. The solution to the equation is $y = \pm 4$, which means that the equation has two solutions: $y = 4$ and $y = -4$.

Why is this important?

Solving quadratic equations is an important skill in mathematics, as it can be used to model real-world problems. For example, in physics, quadratic equations can be used to model the motion of objects under the influence of gravity. In economics, quadratic equations can be used to model the behavior of supply and demand curves.

How can you apply this to your life?

You can apply this skill to your life by using it to solve problems in your daily life. For example, if you are planning a road trip and you need to calculate the distance between two cities, you can use quadratic equations to solve for the distance. You can also use this skill to solve problems in your career, such as modeling the behavior of supply and demand curves in economics.

Common mistakes to avoid

When solving quadratic equations, there are several common mistakes to avoid. One of the most common mistakes is to forget to simplify the equation by eliminating the fractions. Another common mistake is to forget to solve for the variable $y$ after simplifying the equation.

Tips and tricks

When solving quadratic equations, there are several tips and tricks that can help you. One of the most important tips is to simplify the equation by eliminating the fractions as soon as possible. Another important tip is to solve for the variable $y$ after simplifying the equation.

Conclusion

$$

Introduction

In our previous article, we solved the equation $\frac{y^2}{y+4} = \frac{16}{y+4}$ and found that the solution is $y = \pm 4$. In this article, we will answer some common questions that students may have when solving quadratic equations.

Q: What is a quadratic equation?

A: A quadratic equation is a type of equation that involves a squared variable. It is typically written in the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to follow these steps:

1. Simplify the equation by eliminating any fractions.
2. Move all the terms to one side of the equation.
3. Factor the equation, if possible.
4. Use the quadratic formula to find the solutions.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to find the solutions to a quadratic equation. It is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ into the formula. Then, simplify the expression and solve for $x$.

Q: What are the common mistakes to avoid when solving quadratic equations?

A: There are several common mistakes to avoid when solving quadratic equations. These include:

• Forgetting to simplify the equation by eliminating fractions.
• Forgetting to solve for the variable after simplifying the equation.
• Not using the quadratic formula correctly.
• Not checking the solutions to make sure they are valid.

Q: How can I apply quadratic equations to real-world problems?

A: Quadratic equations can be used to model a wide range of real-world problems. Some examples include:

• Modeling the motion of objects under the influence of gravity.
• Modeling the behavior of supply and demand curves in economics.
• Modeling the growth of populations in biology.

Q: What are some tips and tricks for solving quadratic equations?

A: Here are some tips and tricks for solving quadratic equations:

• Simplify the equation by eliminating fractions as soon as possible.
• Use the quadratic formula to find the solutions.
• Check the solutions to make sure they are valid.
• Use factoring to simplify the equation, if possible.

Q: How can I practice solving quadratic equations?

A: There are several ways to practice solving quadratic equations. These include:

• Working through practice problems in a textbook or online resource.
• Using online tools or software to generate random quadratic equations.
• Joining a study group or working with a tutor to practice solving quadratic equations.

Conclusion

In conclusion, solving quadratic equations is an important skill in mathematics that can be used to model real-world problems. By following the steps outlined in this article, you can solve quadratic equations and apply this skill to your life. Remember to simplify the equation by eliminating fractions, and then solve for the variable using the quadratic formula. With practice and patience, you can become proficient in solving quadratic equations and apply this skill to your life.