Chapter A.3, Problem 29E

Solution

To explain why there is no restriction in the reduced form of the expression $\frac{x}{3x-2}+\frac{3}{x-5}$ .

Given:

The reduced form of the given expression is $\frac{x^2+4x-6}{\left(3x-2\right)\left(x-5\right)}$ .

Concept Used:

• A domain is the set of all possible input values for a function.
• To find the domain of a function, set the function equal to y and solve for x . This will give you the set of all x -values for which the function produces a real y -value.
• If a factor is common in the numerator and denominator, then the corresponding zero of that factor is excluded from the domain of the original expression.

Calculation:

Note that there are no factors that are common in the numerator and denominator in the original expression as well as in the reduced form.

So, there is no restrictions in the reduced form of the given expression.