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It takes Austin 8 hours longer than Elliott to construct a wooden chair in shop class. When the classmates work together, they can complete one chair in 3 hours. This situation can be represented by this expression, where t is the amount of time, in hours, it takes Elliott to complete a chair on his own.

It takes Austin 8 hours longer than Elliott to construct a wooden chair in shop class When the classmates work together they can complete one chair in 3 hours T class=

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The equivalent expression obtained using the least common multiple concept is [tex] \frac{6t + 24}{t^{2} +8}[/tex]

To solve, we need to obtain the L. C. M of the denominator values :

The L. C. M of t and t + 8 = [tex] t^{2} + 8t[/tex]

Hence,

[tex]\frac{3}{t} + \frac{3}{t+8} = \frac{6t + 24}{t^{2} +8}[/tex]

Therefore, the equivalent expression which represents the situation described above ls ;[tex] \frac{6t + 24}{t^{2} + 8t}[/tex]

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