Use algebraic manipulation to prove that (x + y) · (x + ) = x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Use algebraic manipulation to prove that (x + y) · (x + ) = x
Expert Solution
Step 1: Solution


We need to prove that:

open parentheses x plus y close parentheses left parenthesis x plus y with bar on top right parenthesis equals x

Solving the Left Hand Side,

L. H. S equals open parentheses x plus y close parentheses left parenthesis x plus y with bar on top right parenthesis
space space space space space space space space space space space equals left parenthesis x. x plus y. x plus x. y with bar on top plus y. y with bar on top right parenthesis space space
space space space space space space space space space space space equals left parenthesis x plus x. left parenthesis y plus y with bar on top right parenthesis plus 0 right parenthesis space space space space space space space space space space space space space space open parentheses because y y with bar on top equals 0 space a n d space x. x equals x close parentheses
space space space space space space space space space space space equals left parenthesis x plus x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses because y plus y with bar on top equals 1 close parentheses
space space space space space space space space space space space equals x

Now, right Hand side,

R. H. S equals x

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