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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q 440 (page 737)

In the following exercise solve $\frac{z}{12} + \frac{z + 3}{3 z} = \frac{1}{z}$

Short Answer

Expert verified

The solution is $z = - 4$

Step by step solution

01

Step 1. Given information

$\frac{z}{12} + \frac{z + 3}{3 z} = \frac{1}{z}$

02

Step 2. Solve

The least common denominator of all denominators in the equation is $(12) (3 z)$

Clear the fraction by multiplying both sides of the equation by the LCD.

$(12) (3 z) (\frac{z}{12} + \frac{z + 3}{3 z}) = (12) (3 z) (\frac{1}{z}) (12) (3 z) (\frac{z}{12}) + (12) (3 z) (\frac{z + 3}{3 z}) = (12) (3 z) (\frac{1}{z}) 3 z^{2} + 12 (z + 3) = 36 3 z^{2} + 12 z = 0 z + 4 = 0 z = - 4$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{\frac{12 c^{2} - 12}{2 c^{2} - 3 c + 1}}{\frac{4 c + 4}{6 c^{2} - 13 c + 5}}$

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?

In the following exercise, perform the indicated operation:

$\frac{c}{c + 2} + \frac{5}{c - 2} - \frac{10 c}{c^{2} - 4}$

Write the steps you would use to explain solving rational inequalities to your little brother.

See all solutions

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