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- https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/11%3A_Fraction_Operations/11.11%3A_Algebra_Connections\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3}, \nonumber \] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp ...\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3}, \nonumber \] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp \nonumber \] \[\frac{2 - \frac{1}{x}}{1 + \frac{1}{x}}, \qquad \frac{\frac{1}{x+h} + 3}{\frac{1}{x+h}}, \qquad \frac{1}{\frac{1}{a} + \frac{1}{b}}, \qquad \frac{\frac{1}{x+a} - \frac{1}{x}}{a} \ldotp \nonumber \]
- https://math.libretexts.org/Courses/Teachers_College_Columbia_University/Book%3A_Mathematics_for_Elementary_Teachers_(Manes)/06%3A_Fractions/6.13%3A_Algebra_Connections\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3},\] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp\] \[\frac{2...\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3},\] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp\] \[\frac{2 - \frac{1}{x}}{1 + \frac{1}{x}}, \qquad \frac{\frac{1}{x+h} + 3}{\frac{1}{x+h}}, \qquad \frac{1}{\frac{1}{a} + \frac{1}{b}}, \qquad \frac{\frac{1}{x+a} - \frac{1}{x}}{a} \ldotp\]
- https://math.libretexts.org/Courses/College_of_the_Desert/College_of_the_Desert_MATH_011%3A_Math_Concepts_for_Elementary_School_Teachers__Number_Systems/08%3A_Fractions/8.12%3A_Algebra_Connections\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3}, \nonumber \] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp ...\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3}, \nonumber \] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp \nonumber \] \[\frac{2 - \frac{1}{x}}{1 + \frac{1}{x}}, \qquad \frac{\frac{1}{x+h} + 3}{\frac{1}{x+h}}, \qquad \frac{1}{\frac{1}{a} + \frac{1}{b}}, \qquad \frac{\frac{1}{x+a} - \frac{1}{x}}{a} \ldotp \nonumber \]
- https://math.libretexts.org/Courses/Hartnell_College/Mathematics_for_Elementary_Teachers/11%3A_Fraction_Operations/11.11%3A_Algebra_Connections\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3},\] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp\] \[\frac{2...\[\frac{(\frac{1}{x} + 1) \cdot x}{(\frac{1}{x}) \cdot x} = \frac{1 + x}{3},\] \[\frac{(\frac{1}{a} - \frac{1}{b}) \cdot a \cdot b}{(ab) \cdot a \cdot b} = \frac{b - a}{a^{2} b^{2}} \ldotp\] \[\frac{2 - \frac{1}{x}}{1 + \frac{1}{x}}, \qquad \frac{\frac{1}{x+h} + 3}{\frac{1}{x+h}}, \qquad \frac{1}{\frac{1}{a} + \frac{1}{b}}, \qquad \frac{\frac{1}{x+a} - \frac{1}{x}}{a} \ldotp\]
