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anemone
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Determine the value of $\dfrac{2k^2}{k-1}$ given $\dfrac{k^2}{k-1}=k^2-8$.
The equation is undefined when the value of k is equal to 1, since dividing by 0 is undefined.
To solve for k, we can set the equation equal to a specific value and use algebraic techniques to isolate k. For example, if we set the equation equal to 10, we can rearrange the terms to get a quadratic equation in terms of k. From there, we can use the quadratic formula to find the two possible values of k.
Yes, the equation can be simplified by factoring out k from the numerator, giving us k(2k-2)/(k-1). From there, we can simplify further if there are any common factors between the numerator and denominator.
Yes, the equation has a restriction on the value of k where k cannot equal 1, as mentioned in the first question. Apart from that, there are no other restrictions on the value of k.
Yes, this equation can be used to solve real-world problems involving ratios, such as determining the cost per unit of a product or calculating the speed of an object. However, it is important to keep in mind any restrictions on the value of k and to make sure the units are consistent in the problem and in the resulting solution.