Math Problem Statement

Solve the following rational equations. Note that your solutions will be graded based on the correctness of your LCD (1 point), correctness of the steps prior to the final answer (1 point), correctness of the solutions/roots (1 point) and correctness of the checking part (1 point). (16 points)

  1. 3 2 y^2 -------- + ------ = -------------- y + 3 y - 2 y^2 + y - 6

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Equations
Factoring Quadratics
Least Common Denominator (LCD)

Formulas

LCD of fractions
Factoring quadratics (y^2 + y - 6 = (y + 3)(y - 2))
Solving quadratic equations (y^2 - 5y = 0)

Theorems

Quadratic Factorization
Zero-Product Property

Suitable Grade Level

Grades 9-12