Final answer:
The ICD of the given equation is the product of the unique denominators (x)(x-1). Multiplying each term by the ICD eliminates the fractions, allowing the equation to be simplified by cross-multiplying, simplifying algebraically, and checking the reasonableness of the answer.
Step-by-step explanation:
The ICD or the least common denominator of the rational expressions is necessary to combine the terms in the equation (5x)/(x-1) - (7)/(x) = (9)/(x). To find the ICD and simplify the equation, we identify all the unique denominators, which in this case are x-1 and x. The ICD is therefore the product of these unique denominators, which is (x)(x-1). Next, we multiply each term by the ICD to eliminate the denominators.
By cross-multiplying, we can avoid fractions and simplify directly:
- Multiply (5x)/(x-1) by (x)/(x), this doesn't change the fraction since any number divided by itself is 1.
- Multiply (7)/(x) and (9)/(x) by (x-1)/(x-1) for the same reason.
Using these steps, we eliminate the denominators and simplify the algebra. Check the answer to ensure it is reasonable, and correct for any mistakes that might have occurred during manipulation.