Calcul alg├ębrique

Fractions


Ecrire les expressions suivantes sous la forme d'une seule fraction:

$A(x)=\dfrac{2}{3x+4}+\dfrac{5}{6x+7}  ;      $B(x)=\dfrac{1-x^2}{1-2x}-\dfrac{1+2x}{4}  ;      $C(x)=\dfrac{3x+2}{2x-3}-1

Solution:


$A(x)=\dfrac{2}{3x+4}+\dfrac{5}{6x+7}
=\dfrac{2(6x+7)+5(3x+4))}{(3x+4)(6x+7)}
=\dfrac{27x+34}{(3x+4)(6x+7)}

$B(x)=\dfrac{1-x^2}{1-2x}-\dfrac{1+2x}{4}
=\dfrac{4\lp1-x^2\rp-(1+2x)(1-2x)}{4(1-2x)}
=\dfrac{4-4x^2-\lp1-4x^2\rp}{4(1-2x)}
=\dfrac{3}{4(1-2x)}

$C(x)=\dfrac{3x+2}{2x-3}-1=\dfrac{3x+2-(2x-3)}{2x-3}
=\dfrac{x+5}{2x-3}


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