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Solve each equation. Check your solutions.$$\frac{1}{x}+\frac{2}{x+2}=\frac{17}{35}$$
$\left\{-\frac{14}{17}, 5\right\}$
Precalculus
Algebra
Chapter 11
Quadratic Equations, Inequalities, and Functions
Section 4
Equations Quadratic in Form
Introduction to Conic Sections
Equations and Inequalities
Functions
Polynomials
Campbell University
McMaster University
University of Michigan - Ann Arbor
Idaho State University
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For exercise 13. We have to multiply everything by the denominators. So I'm going to have 35 X plus 70 plus 70 X. Equal to you 17 X squared plus 34 X. Then I'm going to bring everything to my right hand side. So I have zero equals 17 X. Squared. And It will be -71. X minus 70. Okay then we can factor it as 17 X. & X. And this will be this will be -5. That will be 5085. And so if that's 85 we need to take off 14. So this will be plus 14 to satisfy the conditions. And now we can say x equals negative 14 over 17 And x equals five. Now to check the solutions we have One over negative 14/17 which is the same thing. That's 17/14 negated plus two Over negative 14/17 plus two. We go to 17 over 35. So that's mhm. See over 20/17 Equals 17/35. We can rewrite that as 34 over 20. Better yet 17/10 And then our L. c. d. here is going to be 70. So that's going to be 70 119 minus 85. And That's 34/70. equal to 34/70. That checks out Now let's try five So that's 1/5.7 equals 17/35. It's the same thing as seven plus 10 for 35 And seven plus 10. It is 17. So it's the correct solution
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