Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises: 25

Answer

$x=-\dfrac{1}{3}$

Work Step by Step

$\dfrac{1}{x}=\dfrac{4}{3x}+1$ Let's multiply the whole equation by $3x$, which is the least common multiple of the denominators present in the equation. We'll do this to avoid working with fractions. $(3x)(\dfrac{1}{x}=\dfrac{4}{3x}+1)$ $(3x)(\dfrac{1}{x})=(3x)(\dfrac{4}{3x})+3x$ Simplify: $3=4+3x$ Solve for $x$: $3x=3-4$ $3x=-1$ $x=-\dfrac{1}{3}$
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