Problem 59 - Elementary Algebra

Question

For the following problems, reduce each rational expression if possible. If not possible, state the answer in lowest terms. \(\frac{-3 x+10}{10}\)

Step-by-Step Solution

Answer

Question: Simplify the given rational expression: \(\frac{-3x + 10}{10}\). Answer: \(\frac{-\frac{3}{2}x + 5}{5}\).

Step 1: Examine the expression

We are given the rational expression \(\frac{-3x + 10}{10}\). Our goal is to simplify this expression by factoring out any common factors from both the numerator and the denominator.

Step 2: Factor out the common factors

We can see that both the numerator and the denominator have a common factor of 2. Let's factor that out: \(\frac{-3x + 10}{10} = \frac{2(-\frac{3}{2}x + 5)}{2(5)}\).

Step 3: Simplify the expression

Now that we have factored out the common factor, we can cancel it out from both the numerator and the denominator. This will give us the expression in its simplest form: \(\frac{2(-\frac{3}{2}x + 5)}{2(5)} = \frac{-\frac{3}{2}x + 5}{5}\). So, the rational expression in its lowest terms is \(\frac{-\frac{3}{2}x + 5}{5}\).