Math Problem Statement
2x^2+7x+3/4x+12 perform all operations and simplify
Solution
To simplify the expression , we will follow these steps:
- Factorize both the numerator and the denominator, if possible.
- Simplify by canceling common factors.
Let's start by factorizing the denominator.
Step 1: Factorize the Denominator
The denominator is . We can factor out the common factor of 4:
Step 2: Factorize the Numerator
The numerator is . We need to factorize this quadratic expression.
To factorize :
- Look for two numbers that multiply to and add up to 7.
- These numbers are 6 and 1.
Thus, we rewrite the middle term as :
Now, group the terms:
Factor out the common binomial factor :
Step 3: Simplify the Expression
Now the expression becomes:
Cancel the common factor :
So, the simplified expression is:
Would you like more details or have any questions?
Here are some questions you might want to ask:
- How do you factorize a quadratic expression?
- What if the numerator or denominator cannot be factorized?
- Can you show more examples of rational expressions?
- How do you handle complex rational expressions?
- What is the difference between simplifying and solving an expression?
Tip: Always check if the terms in the numerator and denominator can be factorized before attempting to simplify rational expressions. This can help you identify and cancel common factors easily.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Formulas
Quadratic formula
Theorems
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Suitable Grade Level
Grades 9-12