Algebraic Fractions

Algebra Level 2

2 x + 3 x − 4 − 2 x − 8 2 x + 1 = 1 \large \dfrac{2x+3}{x-4} - \dfrac{2x-8}{2x+1} = 1 Find the value of x x that satisfies the equation above rounded to two decimal places.


The answer is 0.81.

John Smith by John Smith , 15, United Kingdom

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1 solution

Tom Engelsman
Oct 29, 2020

After multiplying the above equation through by ( x − 4 ) ( 2 x + 1 ) , (x-4)(2x+1), the result is just:

( 2 x + 3 ) ( 2 x + 1 ) − ( 2 x − 8 ) ( x − 4 ) = ( x − 4 ) ( 2 x + 1 ) (2x+3)(2x+1)-(2x-8)(x-4) = (x-4)(2x+1) ;

or ( 4 x 2 + 8 x + 3 ) − ( 2 x 2 − 16 x + 32 ) = 2 x 2 − 7 x − 4 (4x^2 +8x + 3)-(2x^2 -16x +32) = 2x^2 -7x -4 ;

or 24 x − 29 = − 7 x − 4 ; 24x -29 = -7x -4;

or 31 x = 25 ; 31x=25;

or x = 25 31 . \boxed{x=\frac{25}{31}}.

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