Find The Value Of This Expression If $x = 3$. X 2 + 3 X − 1 \frac{x^2+3}{x-1} X − 1 X 2 + 3 ​

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Introduction

In this article, we will find the value of the given expression if x = 3. The expression is a fraction with a quadratic polynomial in the numerator and a linear polynomial in the denominator. We will use algebraic manipulation to simplify the expression and find its value.

The Expression

The given expression is x2+3x−1\frac{x^2+3}{x-1}. We are asked to find the value of this expression if x = 3.

Substituting x = 3

To find the value of the expression, we will substitute x = 3 into the expression. This means we will replace every instance of x with 3.

(3)2+3(3)−1\frac{(3)^2+3}{(3)-1}

Simplifying the Expression

Now, we will simplify the expression by evaluating the numerator and denominator separately.

Evaluating the Numerator

The numerator is (3)2+3(3)^2+3. We will evaluate this expression first.

(3)2=9(3)^2 = 9

So, the numerator becomes 9+3=129+3 = 12.

Evaluating the Denominator

The denominator is (3)−1(3)-1. We will evaluate this expression next.

(3)−1=2(3)-1 = 2

So, the denominator becomes 2.

Putting it All Together

Now, we will put the numerator and denominator together to get the final value of the expression.

122\frac{12}{2}

Simplifying the Fraction

The fraction 122\frac{12}{2} can be simplified by dividing the numerator by the denominator.

122=6\frac{12}{2} = 6

Conclusion

In this article, we found the value of the expression x2+3x−1\frac{x^2+3}{x-1} if x = 3. We substituted x = 3 into the expression, simplified the numerator and denominator, and finally simplified the fraction to get the final value of 6.

Final Answer

The final answer is 6\boxed{6}.

Related Topics

  • Algebraic manipulation
  • Simplifying fractions
  • Evaluating expressions

Further Reading

References

Introduction

In this article, we will answer some frequently asked questions about finding the value of the expression x2+3x−1\frac{x^2+3}{x-1} if x = 3. We will cover topics such as algebraic manipulation, simplifying fractions, and evaluating expressions.

Q&A

Q: What is the first step in finding the value of the expression?

A: The first step in finding the value of the expression is to substitute x = 3 into the expression. This means we will replace every instance of x with 3.

Q: How do we simplify the numerator and denominator?

A: To simplify the numerator and denominator, we will evaluate each expression separately. For the numerator, we will calculate (3)2+3(3)^2+3, and for the denominator, we will calculate (3)−1(3)-1.

Q: What is the final value of the expression?

A: The final value of the expression is 6. We simplified the fraction 122\frac{12}{2} by dividing the numerator by the denominator.

Q: What are some common mistakes to avoid when finding the value of the expression?

A: Some common mistakes to avoid when finding the value of the expression include:

  • Not substituting x = 3 into the expression
  • Not simplifying the numerator and denominator
  • Not simplifying the fraction

Q: How do we know if the expression is undefined?

A: The expression is undefined if the denominator is equal to zero. In this case, the denominator is (3)−1(3)-1, which is not equal to zero. Therefore, the expression is defined.

Q: Can we use this method to find the value of any expression?

A: This method can be used to find the value of any expression, but it requires that the expression be a fraction with a quadratic polynomial in the numerator and a linear polynomial in the denominator.

Q: What are some real-world applications of finding the value of expressions?

A: Finding the value of expressions has many real-world applications, including:

  • Calculating the area and perimeter of shapes
  • Determining the cost of goods and services
  • Evaluating the performance of systems and processes

Conclusion

In this article, we answered some frequently asked questions about finding the value of the expression x2+3x−1\frac{x^2+3}{x-1} if x = 3. We covered topics such as algebraic manipulation, simplifying fractions, and evaluating expressions. We hope this article has been helpful in understanding how to find the value of expressions.

Final Answer

The final answer is 6\boxed{6}.

Related Topics

  • Algebraic manipulation
  • Simplifying fractions
  • Evaluating expressions

Further Reading

References