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Solve each equation. Check your solutions.$$\frac{2}{m}+\frac{3}{m+9}=\frac{11}{4}$$
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
Baylor University
Idaho State University
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For Exercise 14. We're going to multiply everything by our 23 denominators. So we'll have eight a.m. Plus 72 plus 12 and equal to 11 a.m. squared plus 99 grouping or like terms will have 99 and -20 am was 79 M minus 72. Well it's plus 79 in an assembly to equal Syria. Alright, so now we can factor this out, we'll have 11 in and and but this was eight, That would be 88 am positive. So we need to take away nine from it. But and that satisfies our conditions. Therefore, n equals -8 or 9 11th. And we're going to check to see if our solutions are correct. So that's going to be two over negative eight plus three over one Equal to 11/4. Um We could also write that with a denominator before as negative one plus 12 equals 11 4th And that means 11/4 equals 11/4. Now let's try it with 9/11. So it's It's going to be 22. 9ths plus three over 9, 11th plus nine equals 11 4th in other words, or have 33 Over 108. And so mhm We can divide I believe 108 53 For T. equals 36. So we'll have 36 here for now this will be 11 plus In 22 times four is 88. So it's going to be 99/36 equals 11/4. Now if we divide everything by nine, that's going to be Going to be 11 of her. four equals 11/4. So both of our original solutions are correct.
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