1960 AHSME Problems/Problem 9: Difference between revisions
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==See Also== | ==See Also== | ||
{{AHSME box|year=1960|num-b=8|num-a=10}} | {{AHSME 40p box|year=1960|num-b=8|num-a=10}} | ||
[[Category:Introductory Algebra Problems]] | |||
Latest revision as of 17:58, 17 May 2018
Problem
The fraction 
is (with suitable restrictions of the values of a, b, and c):
Solution
Use the commutative property to get
![\[\frac{a^2+2ab+b^2-c^2}{a^2+2ac+c^2-b^2}\]](http://latex.artofproblemsolving.com/a/0/d/a0d12f66df908afa863c4390bc0f0aa472e85c08.png)
Factor perfect square trinomials to get
![\[\frac{(a+b)^2-c^2}{(a+c)^2-b^2}\]](http://latex.artofproblemsolving.com/5/b/f/5bf5177bbad0e1e66d007c9cd420af612a9ae8ab.png)
Factor difference of squares to get
![\[\frac{(a+b+c)(a+b-c)}{(a+b+c)(a-b+c)}\]](http://latex.artofproblemsolving.com/6/1/f/61f173cc199d663262416d2cf327a8c9b01d77a6.png)
Cancel out like terms (with suitable restrictions of a, b, c) to get
![\[\frac{a+b-c}{a-b+c}\]](http://latex.artofproblemsolving.com/b/2/4/b2447cde2342e33d8618c330db9d24f78c68b50b.png)
The answer is 
.
See Also
| 1960 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
