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Exercise

$\frac{\left(\frac{2}{t}\right)}{\left(\left(\frac{2}{t}\right)-1\right)}$

Step-by-step Solution

1

Combine $\frac{2}{t}-1$ in a single fraction

$\frac{\frac{2}{t}}{\frac{2-t}{t}}$
2

We can simplify the quotient of fractions $\frac{\frac{2}{t}}{\frac{2-t}{t}}$ by inverting the second fraction and multiply both fractions

$\frac{2t}{t\left(2-t\right)}$
3

Simplify the fraction $\frac{2t}{t\left(2-t\right)}$ by $t$

$\frac{2}{2-t}$

Final answer to the exercise

$\frac{2}{2-t}$

Try other ways to solve this exercise

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  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
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  • Find the roots
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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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