How do you solve $x/(x-2)-1/(x-3)=(1)$ ?

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Answer 1 · 2017-09-11T18:21:38

$color(magenta)(x=4$

$x/(x-2)-1/(x-3)=(1)$

multiply both sides by $x-2$

$:.x-(x-2)/(x-3)=x-2$

multiply both sides by $x-3$

$:.x(x-3)-(x-2)=(x-2)(x-3)$

$:.x^2-3x-x+2=x^2-5x+6$

$:.x^2-x^2-4x+5x=6-2$

$:.color(magenta)(x=4$

~~~~~~~~~~~~~~~~~~~~~~

substitute $color(magenta)(x=4$

$:.4/((color(magenta)4)-2)-1/((color(magenta)4)-3)=(1)$

$:.4/2-1/1=1$

$:.2-1=1$

$:.color(magenta)(1=1$

How do you solve x/(x-2)-1/(x-3)=(1)x/(x-2)-1/(x-3)=(1)?