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Chapter 0: Problem 16

Multiply or divide as indicated. $$\frac{6 x+9}{3 x-15} \cdot \frac{x-5}{4 x+6}$$

Short Answer

Expert verified
After simplification, the final answer is 1.

Step by step solution

01

Simplify each fraction

The fractions can be simplified if they have common factors in the numerator and the denominator. Let's check for the first fraction, \( \frac{6x + 9} {3x - 15} \), it has common factor 3. We divided both the numerator and the denominator by 3, it becomes \( \frac{2x + 3} {x - 5} \). In the second fraction, \( \frac{x - 5} {4x + 6} \), has common factor 2. After dividing both the numerator and the denominator by 2, it becomes \( \frac{x - 5} {2x + 3} \)
02

Multiply the fractions

Now, let's multiply the fractions. When multiplying fractions, we simply multiply the numerators together and the denominators together. Thus, \( \frac{2x + 3} {x - 5} * \frac{x - 5} {2x + 3} \) becomes \( \frac{(2x + 3)(x - 5)} {(x - 5)(2x + 3)} \)
03

Simplify the final expression

The final expression, \( \frac{(2x + 3)(x - 5)} {(x - 5)(2x + 3)} \), can be simplified because it has the same expressions in the numerator as well as the denominator. After cancellation, our final answer is 1 since anything divided by itself is 1.

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Most popular questions from this chapter

Why is \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) not simplified? What must be done to simplify the expression?

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. $$\text { a. } 3^{\frac{1}{2}} \square 3^{\frac{1}{3}}$$ $$\text { b. } \sqrt{7}+\sqrt{18} \square \sqrt{7}+18$$

Factor completely. $$ -x^{2}-4 x+5 $$

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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