Mathematics: Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

The work and answer would be:y-11=3(x-2)y-11=3x-6y=3x+5...

Solve 4/x-4=x/x-4-4/3 for x and determine if - id44443288021, 21121212cutecheytown

Ответ:

ranaawilliamsoowl6dk

10.03.2022

Mathematics

x = 4 (extraneous solution)

Step-by-step explanation:

$\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\$

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back x=4 , we will get two fractions with zero denominator which would be undefined.

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Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

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