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Chapter 0: Problem 23

Multiply or divide as indicated. $$\frac{x+1}{3} \div \frac{3 x+3}{7}$$

Short Answer

Expert verified
The result of the operation \((x+1)/3 \div (3x+3)/7\) is 7.

Step by step solution

01

Change division operation to multiplication operation

Instead of dividing the rational expressions \((x+1)/3\) by \((3x+3)/7\), multiply \((x+1)/3\) by the reciprocal of \((3x+3)/7\), which is \(7/(3x+3)\). Doing so, we get \(\frac{x+1}{3} * \frac{7}{3x+3}\)
02

Simplify the equation

To simplify equation from step 1, first check if there are common factors in numerators and denominators. Here, 3 in denominator can be cancelled with 3 in numerator of second expression. And the binomial \(x+1\) can be written as \(3x+3\) by multiplying with 3. So, the expression becomes: \((x+1) * \frac{7}{x+1}\)
03

Simplify further

In the expression \((x+1) * \frac{7}{x+1}\) from step 2, cancel out the common factors, \(x+1\), in the numerator and denominator. Therefore, the simplified form of the expression is 7.

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Most popular questions from this chapter

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

What is a rational expression?

What is a compound inequality and how is it solved?

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}=49$$

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
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