Math Problem Statement
2/x + 4 = x + 3
Solution
To solve the equation , we need to isolate . Here's the step-by-step process:
Step 1: Subtract 3 from both sides
This simplifies to:
Step 2: Subtract 1 from both sides
This simplifies to:
Step 3: Multiply both sides by to eliminate the denominator
This simplifies to: Which expands to:
Step 4: Rearrange the equation
Step 5: Factor the quadratic equation
Step 6: Solve for
From , we get two solutions:
Step 7: Check for extraneous solutions
Since the original equation contains , is not a valid solution. However, and are valid.
Thus, the solutions are:
Would you like more details on any part of the solution, or do you have any questions?
Here are 5 related questions:
- How do we solve equations with fractions and variables in the denominator?
- What is the method to factor quadratic equations?
- What is an extraneous solution, and why do we check for it?
- How do you complete the square to solve quadratic equations?
- How can we solve quadratic equations using the quadratic formula?
Tip: Always check for extraneous solutions when dealing with fractions in an equation to avoid invalid answers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Equations
Quadratic Equations
Formulas
Quadratic equation formula ax^2 + bx + c = 0
Factoring method
Theorems
Zero Product Property
Extraneous Solutions
Suitable Grade Level
Grades 9-11