Math Problem Statement
Solution
This is an equation involving rational expressions. We can simplify it step by step.
We are given:
Step 1: Factor the quadratic expressions
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The numerator is a difference of squares, so it factors as:
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The denominator factors as:
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The numerator factors as:
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The denominator factors as:
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The numerator factors as:
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The denominator is a difference of squares, so it factors as:
Step 2: Substitute the factored terms into the equation
Now, substitute the factored expressions into the equation:
Step 3: Cancel common factors
We can cancel the common factors in the numerator and denominator across both sides:
- On the left-hand side, cancels from both the numerator and denominator.
- On the right-hand side, cancels in two places, and cancels from the numerator and denominator.
After canceling, we are left with:
Step 4: Cross multiply to simplify further
Now, cross-multiply to solve for :
From here, we can expand both sides and solve for . Would you like me to continue solving this equation or would you like further steps?
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring Quadratic Equations
Simplifying Expressions
Formulas
Difference of squares: a^2 - b^2 = (a - b)(a + b)
Factoring quadratics: ax^2 + bx + c = (mx + n)(px + q)
Theorems
Cross Multiplication for Equations
Properties of Rational Expressions
Suitable Grade Level
Grades 9-11
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