Math Problem Statement

Find the equations of both lines that are tangent to the curve 𝑦𝑦 = 𝑥𝑥−1 𝑥𝑥+1 and are parallel to the line 𝑥𝑥 − 2𝑦𝑦 = 2. (

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Quotient Rule
Slopes of Tangent Lines

Formulas

Quotient Rule for Differentiation: (u/v)' = (v(du/dx) - u(dv/dx)) / v^2
Point-Slope Form: y - y1 = m(x - x1)

Theorems

Tangent Line Theorem

Suitable Grade Level

Grades 11-12